I would ask this question on the veggie garden forum. This Maine forum tends to be quite slow. If it were my compost, I wouldn't since mine is a cold compost pile. I don't know if the fungus spores are likely to be killed by a hot compost pile, but perhaps you can get an answer from the folks on the veggie forum. If not, I would probably toss them, since that is the usual advice for fungal diseases such as those that effect peonies and strawberries.

Not recommended