Grafting cultivated plums onto wild plums can indeed be done... and I have a photo to prove it!
This year I decided to try an experiment. I planted a Chickasaw plum in my front yard a couple of years ago. Being a tough Florida native, it's grown like a weed and suckered wildly.
Before it leafed out this year, I took some bud wood off a couple of improved Florida plum varieties and grafted them on to some of the suckers. Out of five tries, it seems that at least two have taken... and the one in the picture has really flown.
There are native plums all over the place. They produce small, tart fruit that are mostly eaten by the birds... yet the trees are carefree and grow in terrible soil. It's interesting how different the leaves are on the improved types... big green leaves instead of the tiny green and red leaves of the Chickasaw plum.
Why not take advantage of their hardy nature and graft in some big, sweet plums? It's too late for this year, but it would be a good February project to try in 2015.
I'm certainly going to graft some more varieties onto the suckers in my yard. I might even guerrilla graft some on trees around the neighborhood. All you need is a good donor tree for bud wood, some grafting tape and a sharp knife.
Here's the grafting tape I use (thanks, Amazon!)
Poly Budding Tape