@T(h)ink
Lol - no, I don't think so, the name is based on "la volte" (FR) and "la volta" (IT) [both stand for turn, turning, also in domains like hippism and fencing, for instance - from popular Latin "volvitare"].
The name "La Voulte-sur-Rhône" (Occitan La Vòuta) has the same origin, but could also refer to "bow", "arch" (= la voûte - architecture) or to "tower" (= tour - architecture - in the Quercy region).
And the volte (dance) seems to have been derived from the "gaillarde".
Maybe that the bourrée was a rather modest dance, but the "pas de bourrée" is a sequence of ballet steps, i.e. beating steps.