No. Probably the only thing you could consider dead heading too much would be removing too much foliage while dead heading that it slows the plant's ability to feed itself and recycle. Keeping the spent flowers cut off will prevent seed set which SHOULD help it repeat its flowering faster...as long as it is receiving the required resources to accomplish that. Otherwise, keeping the spent flowers picked or cut off will keep the plants looking better and help you keep an eye out for any other potential problems before they settle in and become established. Just don't go whacking off arm loads of foliage when you remove the spent flowers. The more leaves, the more food and the faster it is going to mature and repeat the bloom.

Thanks roseseek :) That’s what I figured. I’m trying to only cut the blooms and no leaves for now. They’re all growing new branches or leaves. Some I can’t tell, but lots of reddish new growth and flowers over and over. I’ll keep at it with the buds so they can focused on getting established

You're welcome. Enjoy!

If your roses only seem interested in growing and blooming then I'd say you're doing it right! Unhealthy, unhappy roses do not grow and certainly do not bloom! Stop worrying about growing the roots. A rose will not produce more growth or blooms than it feels it can support with its existing root ball.

Thanks Seil :) I'll let them do their thing and hopefully continue growing/blooming!