They'll be fine. If root system is intact it will produce new growth.
Actually, flowers of first year rooted cuttings had to be pinched off anyway. You don't want plant to spend energy on flowers, top growth and roots is your main concern this year.

Thanks, ego45. I wondered about the blooms. I guess I should lop them off the other plants as well.

How about this question. I brought in the chopped branches with flowers, and put them in water. If I chop off the blooms, apply a little rooting gel, and pot up the branches, can they root? Two are merely current green wood with small blooms on top and a few leaves, and one is a length of the original cutting, with two blooming green wood branches and some leaves.

Thanks for your help.

Personally, I never tried to root soft wood (green) cuttings, but hard wood rooting (March-April) brings almost 100% results and semi-hard wood (August-September) around 50%.
Try, you have nothing to lose.