Yes, this is a mulberry. Please make sure you have a proper identification before eating any plant. Some environments have few poisonous plants, others a lot. Past my warning, you can easily propagate those by stem cuttings. They root very easily.
The maypop is wild everywhere here and I use them on unproductive trees because they die to the ground each winter. They also do not outcompete with the trees. When I pull the vines out at the end of the season I dry the leaves for a nice calming tea.
I keep all my trees close to around 12 foot tall. My orchard spacing is close and narrow and so shorter trees work best for me. Smaller fruits on bigger trees like Autumn olives can be shaken off though.
Considering most orchard trees may not grow true to type and most areas in the States have access to apple/pear/plum/etc wild rootstock it doesn't make sense to grow from seed what we can dig up. I can see valid arguments for several tropicals, but if you have access to usable rootstock locally I suggest digging them up.