I cant imagine a new chain will be skipping on those chainrings, they are not shark toothed at all.

sure, as noted, if some wear has occurred from too long chain left on too long, then it may affect a new chain, in terms of accelerating chain wear, but I guess the only way to know is to put the new stuff on and see.
I would guess that it will be fine.

and the whole "keeping the drivetrain clean ish" thing certainly does help wiht long term wear, but thats up to you. Generally, doing the regular , fast and easy rag wipe of stuff at least keeps the excess chain lube down, that always comes out on its own, and all it does is have dirt stick to it, and makes the gunky, gritty paste that was on everything.