They can. It's mostly a function of what rootstock they are growing on. Usually they don't have many suckers.

The Fruitnut

My Evans sour cherries do sucker allot, just like aspen, the lawn mower takes care of it.
You can find out when digging out, see if the roots are attached to the tree root,... this will be a sucker.

Konrad

Yes, some root stocks do this quite a lot.
Just for the sake of clarity, suckers are the branches that come from the lowest part of a tree, below the graft. new sprouts that come up from the roots an make a new tree are called just that, a new tree, or sprouts, and that sort of root is called "precocious"
Certain cherry root stocks do this more that others. One of the newer dwarfing stocks is especially bad as I recall.
My jujube are very bad about this, but then I use the sprouts to graft to, to start new trees.
when trying to get rid of these precocious sprouts, be sure to dig a bit and make a clean cut right at the root that is running horizontally in the ground. Try to cause as little injury to the horizontal root as possible, or it will sprout out multiple new sprouts again and again.

This sounds like my Evans cherries, [grown on their own root], these root suckers,
[a natural way of reproduction]
can be transplanted on a new location, in my case,
I grow a hedge and mow both sides.
Never use a herbicide on these, it can kill the parent tree.
Konrad

Hello all, where are all your trees grown? I live in California and I have a cherry tree that has never given fruit . I planted it around 5 years ago . What do you think .

Yes, our yard is FULL of runners from our one tree.