No, this is a very common misconception that if a bullet strikes a combat helmet, even if the helmet stops the bullet that it would break your neck. Read more to learn why!
Combat helmets employ a passive momentum defeat mechanism in which a soft-cored bullet with a small mass and high velocity progressively engages a larger mass of high-strength fiber/resin composite, decreasing the bullet velocity and locally transferring momentum to the helmet. This process continues until all the momentum of the incoming round is deposited into the helmet or the helmet is defeated and penetrated by the incoming round.  Momentum aside, the projectile, suddenly slowed down, transfers kinetic energy equivalent to hundreds or thousands of joules onto the helmet in less than 1 ms.
Cervical injuries are commonly caused by high-mass, low-velocity, high-momentum events -- e.g. automotive accidents or sports collisions. Ballistic events are qualitatively different, in that they're characterized by high strain rates combined with low momentum transfer (low mass, high velocity), and behind-armor ballistic trauma does not result in familiar patterns of wounding. Cervical injury is particularly unlikely. Consider: Compared to a rifle round impacting a helmet, a typical football head contact would transfer anywhere from 12 to 100 times the momentum, thus causing much greater overall head and neck motion and more global internal brain deformation.  When a small-arms projectile impacts a combat helmet, almost entirely regardless of caliber, momentum transfer to the helmet wearer's head and neck is negligible.
Experiments were run where human cadavers wearing combat helmets were hit on the helmet, at various points on the shell, with 9mm FMJ rounds at up to 1510 feet per second. Follow-up assessment indicated that there was an extremely low risk of neck injury, and no neck injuries were observed in the experiment.  This experiment’s point is sharpened on account of the fact that cadavers are generally more prone to exhibiting signs of injury than living people. This is because the average cadaver, at roughly 75 years, is far older than the average military trauma patient, which is about 26 years.  Cervical bones become more brittle and weaker with age, and an old cadaver’s cervical vertebrae should be expected to fracture at lower impact energies than the average military trauma patient’s.  That no neck injuries were apparent in cadaver studies is a good indication that none should be expected in helmet-wearing men of military age, and validates the notion that low momentum transfer implies a very low potential for neck injury in combat helmet impacts.
The National Research Council's Board on Army Science and Technology has reviewed the data in question, and, in a report reviewing the relevancy and quality of combat helmet test protocols, estimated that the risk of neck injury upon impact from a 7.62×54 mm rifle threat is less than 0.1 percent. The board estimates it would still be under 25 percent for a .50-cal threat at current helmet areal densities. 
Despite low momentum, bullets have extremely high kinetic energy density. Upon contact with a helmet shell, the KE of the projectile is locally expended through damage mechanisms such as fiber breakage, matrix cracking, delamination, fiber buckling, friction, and conversion to heat. These mechanisms necessarily result in helmet shell deformation, which can result in injury if the shell comes into contact with the skull. For this reason, the standoff between the head and the helmet shell interior in current helmet systems was designed to be 0.5" (13mm) or greater , and military test protocols mandate that helmet backface deformation can measure no greater than 16mm for crown, left, and right impacts and no greater than 25.4mm for front and rear impacts.  If you want to learn more about some of the current advances to combat KE check out this blog!
The ceramic up-armor plate dramatically improves the kinetic energy absorption capabilities of the helmet shell. Upon contact with the ceramic layer, the projectile’s kinetic energy is transformed into the plastic deformation of the projectile via shattering or erosion, brittle fracture of the ceramic, plastic deformation of the backing layer via the aforementioned damage mechanisms, and heat. The fact that the ceramic plate shatters steel-core rounds enables it to defeat threats such as the M855, and light AP rounds such as the SS190. The fact that the brittle failure of the ceramic tile is a highly efficient energy-sink, and spreads out the projectile’s residual kinetic energy upon a broader area of the helmet shell, enables it to defeat very high-energy rounds such as the 7.62x39mm MSC.
In any case, one of the foundations of backface deformation testing is equivalency. If one observes 25mm BFD when a 9mm round hits a Level II armor panel, and also observes 25mm BFD when a 7.62x39mm Ball round hits a Level III plate, the likelihood of blunt impact injury is identical in either case. This is why BFD limits are typically constant across threat levels.
The ATE2+UpArmor combo can stop rifle threats with less than 25mm BFD, and in some cases much less. It handles full-power rifle round impacts in precisely the same way that other combat helmets handle impacts from the 9mm FMJ. Although the rifle round will deliver slightly more momentum, it is still negligible overall, and far from enough to increase the likelihood of injury to any significant extent.
- Bullets have low momentum, and small-arms impacts onto helmets are unlikely to result in significant head and neck motion.
- The overall risk of neck injury from small-arms impacts onto helmets has been estimated at less than 0.1%, even in a worst-case scenario where a helmet is impacted by, and stops, a 7.62×54 mm projectile.
- Skull and brain injury due to backface deformation in a significant risk whenever combat helmets are impacted by small-arms projectiles, but the HHV ATE2+UpArmor combo has proven capable of defeating full-power rifle threats with BFD kept well within the limits set by current military and civilian standards.
- Thus the ATE2+UpArmor combo handles the rifle threats in exactly the same way that standard combat helmets handle pistol threats. Without increased risk of head or neck injury.
If you would like to learn more about wartime head injuries and history of them. We have a seven part blog series starting here - Wartime Head Injuries and Helmets.