Yeah, that's the thing. A lot of rules about the House have been formed over the years and are not from the Constitution. You won't find the Hastert Rule in the Constitution, for example.
Yeah but when in doubt go with the Constitution. The default assumption should be party is not a prerequisite. Confirmation shouldn't cause surprise.
FYI the "Hastert Rule" isn't in the Constitution... and is ignored at times. So you're proving my point. You asked "can". And yes a lot of things "can" happen according to the Constitution. That doesn't necessarily mean they are likely to happen.