my thumb muscle [bottom left of my left (fretting) hand] had been acting up after elongated playing for a few days, so i decided to trying playing with my hand on the back of the neck for a bit. i wanted to play more with my thumb on the low E string and i wondered if this would be helpful for this?

can it be bad for me playing in both this and another fashion? or any other draw backs or what have you
no it's fine. for metal i put my thumb on the back of the neck, but for blues and other stuff with feeling in it i put my thumb on the low E (there is some switching back and forth), plus it helps with bends.

Ibanez RG7621
Ibanez RG121
not an issue as long as you are not pressing down very hard with your thumb.

placing the thumb on the low E can help with muting and adding certain bass notes to some chords so it is actually very useful