it works exactly like you think.
if collection power is the only thing you are missing for ranking up and u rent cards with enough power, you will rank up.

For example:
i played diamond league with many rentals and only cos of my ranking and the power through rented cards, i was able to hold the league.
Now my rentals are gone (i let them run out) and then i sat at bronze with 3,300 rating.
And as far as i know, it is intended to work that way.