My Neo. 'Leesburg' is putting out about 8 or 9 new shoots and I'm contemplating removing one to try in S/H.
Most of the new shoots do not have any roots associated with them and a few shoots are producing roots out of the middle of the main stem, so to remove them, I would have to basically cut the top half of the plant off.
I agree with above...WAIT! I have never seen an orchid grow without some roots. Houseplants yes, but not an orchid. Good luck and enjoy what you have. More growth, more flowers.