This is certainly possible - and I am vigilant for any signs of stress/pain in my neck - both during/afterwards/next day. The known issues with my neck didn't arise until last October, though there was likely some underlying problems with it prior to that point.
This is one reason I am not doing weighted back squats - the squat machine seems to actually stretch my neck and it feels better afterwards than before. All in all my cervical spine seems to feel better than it did before I started with the new group trainer almost a month ago and he is aware of my neck issues. I have't needed to use heat on my neck since we started - and prior to that I was using it several times a week.