Can't see why not? This is a common occurrence in compost bins especially on allotments. They like the warmth that the heap provides. Just make sure that you remember to wash your hands well after handling compost.
I would Google Leptospirosis, Weil's Disease just to be aware of possible implications.

I see no reason why you can't use the compost for your veg. Personally I'd wear gloves whilst handling but i know others who wouldn't.