It is possible to do the croatian part of the Parenzana only with a mountain bike. In this page you can find some GPS tracks and a useful map of drinking fountains.
Map of some drinking fountains around this track. It is possible to go from Monfalcone to Motovun in a single day, going slow, for a not so trained average young human being. I think, but I never tried, that it is possible to do also the full Parenzana starting from Trieste in a single day for a trained person.