Not hardly --- one genus cannot give rise to another genus --- it just doesn't happen.
True, but some Creationists hold that there are some things that evolution just can't do (e.g., cetaceans could never have evolved from land animals). Some even hold that God imposes a 'genetic barrier' such that some mutations will never occur.
Not even close --- the biggest boundary in existence that is against evolution is time.
Fortunately, we've had plenty of that. Bacteria can evolve to ingest and metabolise new, and even artificial, food sources in a matter of decades:
E. coli have been seen to evolve the ability to ingest citric acid in two decades, and there exists a type of bacteria that can metabolise nylon.
But that aside, even if fungi had eternity to operate, I don't believe it would eventually lead to mankind.
Actually, if they had an
eternity, they would inevitably evolve into a species that is indistinguishable from humans. It would take an unimaginably long time, but they
would do it.
Even if we put a time constraint on things, they are still capable of evolving sentience and sapience on par with, or even exceeding, humans.
To be truthful, I never heard of Theistic Evolution until I came here; and I notice now when my pastor or visiting missionaries speak, they haven't made mention of them, either.
I can't, to this day, fathom why anyone would mix the Creation with evolution --- or even want to.
Judging from those I've talked to, they generally want to reconcile their religious beliefs with established scientific knowledge. The evidence
is overwhelming, and how Creationists react to it tells us a lot about them. Some stick their fingers in their ears and spread a load of half-baked lies (hello, Mr. Hovind), some cave completely and throw out their religious beliefs, and some strike a compromise.