Probably not - this is a tree which wants to get 25 feet tall, and when it does, the flowers are always in the top third, never lower down. You can try it if you like, but you may simply encourage shooting off the rootstock, which you don't really want.

Maybe the first 2 or 3 feet of the three is the rootstock, but usually the graft is lower down than this. If it is the rootstock then that's why you're not getting any growth. Check to see where the graft is. This should be visible and it looks like a bulbous growth on the trunk.

You don't want any branches to grow below the graft as this growth will revert back to the type of cherry that was used for the rootstock.

You don't say how tall your tree is. The flowers, and ultimately the fruit, will grow on new growth. As Bamboo said, cherry trees can grow quite tall so it stands to reason that most of the new growth will be higher up the tree where the fruit will form.

If your tree is quite tall, then prune it in the winter when it's dormant. You can prune it to reduce the height and cut back any side branches. Remove any branches that cross and generally open up the tree for more light and air to circulate.

The graft on Prunus amanogawa is at the base, Myron, and this one doesn't put out branches really, it doesn't have a spreading crown, it literally grows straight up, hence the common name 'flagpole cherry'. Any 'branches' also point straight up.

I've grown it myself, love it, plant it wherever possible, usually planting a clematis to scramble up by meshing up the lower portion that's bare of growth so its a bit more interesting in summer (not possible in a pot).