The scion is best dormant because it needs two weeks to heal in so that it can be water from the roots. The rootstock is best after it starts growing because that hastens healing. Give it a try, might work.

That was what common sense seemed to suggest, but why then is scionwood typically collected so early?
Is it just that in some places plants come out of dormancy sooner and general recommendations try to make one statement of timing for everyone? Or are there things happening in the trees in the early spring that I just can't see?

For me in zone 5 I'll collect scions in March. I prefer to graft to a tree or rootstock that is already awake. Last year I grabbed some scions from a friends tree that were starting to bud out and those took. I don't know how late you can push that.