I'm interested to know of other projects where this situation has come up. Would you recommend this? Or should each team have only one QC tester?
I never recommend that anyone be split among any number of teams, period.
When you have an insufficient number of people, testers, DBAs, UX people, you have an impediment. The team needs to raise that impediment to someone who can resolve that impediment. In the meantime, the team needs to work around that impediment.
That means the team needs to do the testing itself. So the team without the tester has to do all the testing itself. And, the team with one lonely tester has to do lots of other testing, because a team with, say 3 or 4 developers and 1 tester, might have too many developers for that one tester.
Agile teams watch their work in progress and the quality of their output, their features. They can't say, "I did my part and handed it off to whomever." They say, "We worked together on this and got the whole darn thing to done."
It's a difficult problem, and one that arises often when teams start their transition to agile.