I'm curious why many of the welds, including factory ones, are spot welded instead of full length beads along all joints. I'm assuming that it just not necessary, but I think it does not look as pleasing.
In a case like this, if you don't weld it full length, it may be strong enough, but you create a "corrosion hot spot" due to the bare metal areas between the two pieces. No matter what you do, eventually rust will come out of this area, because capillary action will draw and hold water in there.
If your tractor is stored indoors and not used during the foul weather it may not be an issue for a long time.
If you don't weld it full length, clean the remaining areas and chalk them with an auto body seam sealer, before you paint it. This will give a
reasonable amount of protection, but is not a replacement for full length welds.
There are also coatings made to be used as a "primer", before you weld it, that help. I don't like them, they can interfere with the welds. This mount of heat, in such a narrow area, will likely burn most of it off anyway. However, some guys swear by them.