I’m really not enough of a politics junkie to know when this maneuver was used for the final language of a bill and when it was used for something else. It seems clear to me, however, that if the maneuver is constitutionally OK for one kind of House resolution, it’s OK for every kind of resolution.

Nothing is being “passed without actually being voted on”. There will be one vote, which will simultaneously have two effects: one described by the procedural rule, and one described in the text of the bill itself. Every Representative who votes on the bill will be perfectly aware of those two effects and can choose to vote yea or nay accordingly. And then the majority will rule, which is more than we get from the Senate.