I hope you realise that most flowering cherries are grafted onto a rootstock which is different to the above ground part of the tree. I think that most Cherries in Australia are on Mahleb or Mazzard rootstocks but I see there are some more recent rootstock that give smaller trees and may be being used by now.
My point is that suckers grow from the roots so they will be the rootstock variety, not the flowering cherry that you know. You can still grow it as bonsai, it will probably be hardier than the flowering var. It will flower but won't have the same flowers as the tree you have in the garden.