So, in normal poker, assuming you start by posting in the BB, the proportion of hands that you play in the BB is never less than 1/(# players seated), one ninth for example at FR.

This isn't the case for Rush poker. Because everyone starts their first hand in the BB, and most leave before they would have been in the BB next, those playing shorter sessions bear a somewhat larger proportion of BB hands.

This effect isn't that big: I play 8-10 hr sessions and I've been in the BB 97.95% as often as I should have been. For someone with a serviceable but unspectacular winrate around 4 bb/100 (2ptbb/100), this reduction in big blind spots adds something like 0.1 bb/100 in winrate. I realize that this is about an extra 1$/hr at 100NL FR, but still...

You always start in the BB?

unless someone else at the table is also playing their first hand, in which case it picks between you randomly.