So I just found this glitch with the Shadow Mod that allows you to walljump without using the homing attack first, by using the homing attack, then restarting the level before touching the ground, basically Shadow stays in the state of "grabbing the next wall he touches" which obviously he shouldn't be able to do at the very start of a level.

It works with both "Last Checkpoint" and "Restart Act".

It feels to me like it doesn't fit in the IL way of doing things, but I'm not sure if I can use it or not.

Video showcasing the glitch:

I would say no, essentially the IL should be treated as if it's started from scratch, this is essentially carrying something from a previous attempt.