First time I was forcedly switched to the snake, I observed that it skipped 14 German skills, and the progress on the snake was marked on Duome as getting to L2 (red) — from L0 on the initial (recently extended) tree, while I already had all the tree up to the end at L1 (blue), and while I were doing lessons from the snake, I observed that my crown count was lower, i.e. the crowns for the skills which were mapped to the snake unit I was doing were zeroed, and I had to redo the same skills from L0 instead of from L1.
When it was possible to return to the tree thanks to www-internal, I finished the same German tree to L3, but noticed that the snake didn't show any progress and stuck more or less at the same place where I quitted it.
When recently www-internal was inoperative for some time, I did lessons from Duome tree to L3 and higher—which are unaccessible from the snake at all!—but lost about 100 crowns in total (German and French courses). Funny that just an attempt to do a lesson on www-internal partly restored the crown count, and when www-internal was back, all my crowns were back, too (perhaps less 1 or 2).
My theory is that the tree status was mapped onto the snake only once, at the moment of transition, and later, even if the instructive lessons were done from the tree, but repetitions and check-points not, it doesn't count, and if you return to the snake, you'll lose the crowns and have to restart everything from zero (L0).