Yes, my red jaboticaba has lots of suckers. I have several suckers that are probably 2 feet tall on one of mine, but all the little ones I try to pick off. I try to cover the exposed roots so that they don't sucker but still end up having some. I haven't seen any of my other jaboticaba have suckers.
How are the suckers doing? I took a few off my red but seedlings seem to outperform my suckers very quickly. The suckers take a long time to establish away from the mother plant.