Is it possible for me to iron a cross-stitch pattern after I have sewed beads on it?

The beads I am given are plastic beads.

Yes if you are careful!!
You need to iron it wrong side up with a towel under it to cushion the beads.
You need to make sure though that the beads aren’t plastic if they are they will melt!! But most beads used for cross stitch are glass and they should be fine
Hope this helps

Cross Bead Necklace