But if you have a yard tree that produces new suckers continuously, can
those same suckers be used as cuttings for propagation purposes?

Sure, if you want a bonsai that produces suckers continuously.

Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)