If so, to what extent?
I personally never bothered. Whenever I try, I fail miserably. I prefer RPGs with strong mechanics so that the game effectively does the roleplaying for me. e.g.:
- Instead of pretending my character is weak and can't handle heavy weapons, my preferred RPG will have a mechanic that limits heavier equipment to characters with high Strength.
- Instead of pretending my character has to autistically eat, drink, and sleep, my preferred RPG will have needs mechanics that force me to eat, drink, and sleep... or better, not have them at all because these mechanics usually suck and are completely negligible.
My roleplaying begins and ends at the character creation screen. Afterwards, it is the limits that the game's mechanics impose on my character who define who they are.