i know that i should never tune my guitar to drop c without adjusting the action, however, one of my friends told me today that he never changes the action and only uses big strings when down tuning.

is there a problem if i use thicker strings but don't adjust the action at all?
i don't want a warped neck

i plan to do this on my Epi LesPaul btw
ceci n'est pas un guitariste.
who told you you should never tune to drop c without adjusting the action? if you like the action how it is when your tuned to drop c, then keep the action. the action wont help your neck from being warped, that's where the truss rod comes into play. If you move up in guages, you might need to adjust your truss rod, but only if you notice a slight bow or something. if your neck reacts fine then there is now need.