Hi,
They can root ; it all depends on what you're calling a root-sucker ( one week popped out root-sucker ? one full season old ?).
This is what I would do: Keep the suckers and remove them with roots come next May or June and give them by then.
I would do this especially if the root-suckers popped out this season as they are green wood and that's a misery to keep those alive. You could be lucky too and root them all ...
It is a matter of odds.
I would edge my odds and act in May , except if you're urged to give the cuttings and people won't come back to you asking for more, because the first ones died ...
Depending on the strain root-suckers may take longer to fruit.
But on a non grafted tree, they will be a copy of the mother and fruit like herself ... Except for some possible small mutations .
I've got a weeping one for instance... She's the only one with weeping branches ... out of 50+ .