Yup, I've been doing this for my entire life, treating games of any possible genre like RPGs. Making up a backstory for my character, creating their personality in my mind and acting accordingly. So yeah, I can imagine playing a character who's obsessed with collecting bear asses even if it doesn't influence the plot or gameplay...
...well, sometimes I took things too far. I remember one GTA4 run when I played as Repentant Niko who obeyed all traffic laws (you know, stopping on the red light and so on) because he was so sorry about his past as a criminal (and war criminal).