if I cut down a young friut tree will a sucker pop up and regrow the tree? would a plum tree do the same?

Exactly, what pops up may not even be the same type fruit: my quince died and the roots were apple, so now I have an apple in it's place. Dwarf trees may be grafted onto a partially incompatible root stock to keep the top from growing up to potential. As an experiment, yes you can, but you might not like what pops back up.

Often times fruit trees are grafted on to another similar fruit root stock.

If you get a sucker from the root stock tree, you wouldn't have the same tree at all.