As a beginner lead, I guess I might be able to contribute here...
First, as far as I can remember, both my teacher and taxi-teacher(s)
do do a count through of beats as we go through each move.
They will tell us how many beats each move is, count through them as they're demoing them, count as we do them, use "beat words", all that good stuff.
I, as a learning lead,
think I'm getting it right when it comes to actually dancing these moves, but you'd have to ask my partners.
That said, any talk of numbers goes in one ear and out the other. Why do I need to know that the first move has 7 beats?* Why do I need to know that I wrap on the 3rd beat of the basket?* Just so long as I'm doing it right, it shouldn't matter, should it?
* Would getting these numbers wrong help prove my point?
Cheers!