It's a difficult question to answer because it depends on the real degree of 'somewhat' and its location. If the driving flank of the thread's eaten away over a turn or more, and it's in the area where the tollpost or toolholder would be around 1 to 15 cm from the chuck face, then it's serious and likely to gall or score the corresponding halfnut flanks.

What condition are the halfnuts in already, anyway? What assurance do you have that other significant components aren't affected?

If it really is only surface corrosion and really does affect only the leadscrew it's unlikely to cause a serious problem, even if you do use it to cut threads – but it's hard to see how you're gonna know without close examination.

Yes, it looks as much worn as corroded. Try closing the halfnuts on the worn bit of thread and check that the saddle is held solidly and won't rattle along the leadscrew under drive from the saddle handwheel, even if there's noticeable end float. Or get the owner to do so if you can't get to the lathe yourself.

Also try turning the end handwheel or heastock gear with the halfnuts closed and see if it drives the saddle along. Clamp the saddle and check that trying to turn the leadscrew doesn't pop the halfnuts open.

If it passes this lot, it'll *probably* do what you want.

Good luck with your new purchase and welcome to a whole new hobby of fettling antique machine tools. Be careful. It can take over your life.