My initial reaction, like that of most other AE speakers and apparently also some BE speakers, was that 'their' just seems out of place, and that 'in droves' is more common as a fixed expression, period.
On further reflection, I might wonder if 'in their' could have been older and more poetic or literary, perhaps normally following the definite article, that is, certain specific things in their large numbers, as opposed to just some or a lot of indefinite ones. Bion may also be on the right track to think of larger numbers. I could imagine, say, a line of poetry about 'the stars in their millions' or 'the cherubim in their wingèd squadrons' or something.
But smaller numbers ... The eggs in their dozens, stacked placidly on the refrigerated supermarket shelves? Noah's animals in their twos, boarding the ark? Hmm ...
Let's just say I haven't yet thought of a context in which 'in their dozens' sounds idiomatic to me.