Rusty Worn Agitator Shaft
Yes this shaft will work, BUT the top seals in your new basket drive assembly will quickly be ruined, so if this is to be an every-day-driver it will only last a year or so before you have problems with moisture getting into the agitator shaft bearings and possibly the transmission.
If you want to use this machine much get a NEW or at least a nearly perfect used one, if you use a used AS from a post 1980 machine the top seal area that is in bad shape on your shaft is nearly always perfect because the spin-tube was 6" shorter so there is never any seal wear near the top of the shaft.
John L.