I want to take some New Vegas Medical Center implants, and I'm wondering if by raising a Primary Statistic I can go over the skill cap.

In other words, if I already have 100 Energy Weapons, if I raise my Perception would my skill with energy weapons increase any further(even though it doesn't show on the Pip-Boy)?

No, not to any effect.

However, I believe that the game remembers that you have a bonus over 100 and if you then receive a penalty for any reason, the bonus will offset that penalty.

So if you then got a -1 Perception penalty from withdrawal, your skill would stay at 100.

I dont believe so, just guessing here

It does remember your points beyond 100. Its just that your effectiveness with that skill doesn't go over 100. In Fallout 3, the exception was Unarmed. I'm not sure if any of the combat-based skills get more effective over 100 or not in New Vegas.

I don't think so, I believe it's just the offset for any negative modifiers...