Yeah, tost can either be the noun "toast" as here or an adjective "ill". Both appear to be borrowings. The "ill" meaning is the older, from Latin tostus "toasted, scorched, parched", so you can see how it came to eventually mean "ill". The "toast" meaning was borrowed later from English toast, which of course is a borrowing from the same Latin word via Old French.
The idiomatic He's toast i.e. referring to someone as being "burned, scorched, wiped out, demolished etc." was a much later development in the English language.
This means that although there isn't a direct relationship between "He's toast" and Welsh adjectival tost "ill" in the sense that one is derived from the other, it does show how Latin tostus developed separately in the two languages to mean different but somewhat related things.