Yes, absolutely. And I feel that moral absolutism of the alignment is counterproductive for this sort of exploration.
Why? Surely this is a fallacy.
There would be nothing wrong with you playing a PC in my games (in which there is objective good and evil, as already defined) that engages in murder, torture and worse for a 'greater good'
and who genuinely thinks he is good.
Just don't expect to be using a Talisman of Pure Good, or to be dealing radiant damage with your Spirit Guardians.
Just because the DM (and the game world) has a different view of your PCs actions and alignment than the Character themselves would do, doesnt mean you cant explore those nuances.
Hypothetical
You're playing a PC who is a genocidal monster, but he only does it for some noble purpose (as all genocides are) such as 'annihilating an enemy that poses an existential threat to your homeland' like a local nation of Orcs who constantly raid and are in thrall to dark gods.
Your PC is also an honorable man, who respects family and tradition. He is a loving father and husband, but a coldly merciless monster to the Orcs, whom he tortures, crucifies, and slaughters down to the women and the children whom he tosses on pyres while alive.
You have LG written on your sheet, and your PC genuinely thinks he is good.
Your DM however secretly notes you are (in fact) LE due to your actions (in so far as it's relevant to any game effects, or what afterlife you wind up in).
How does this affect your exploration of this character in any negative way?