I've been aware of Ertai's Meddling for a long time, and wondering if anything interesting
- moreso than just ​ ​ ​ "the other spell does nothing, even though that other spell would normally do something" ​ -
could happen as a result of Ertai's Meddling allowing a spell that can't be cast in an upkeep to nonetheless resolve in an upkeep.

I believe I have now found a card where that is interesting: ​ Illusionist's Gambit

Does the combination result in a turn having a combat phase before its first main phase?

I think yes,

Ertai's Meddling puts the card ​ ​ ​ "onto the stack as a copy of the original spell" ​ , ​ ​ ​ rather than casting anything.
Illusionist's Gambit adds the additional combat phase ​ ​ ​ "After this phase," ​ rather than the ​ ​ ​ "After this main phase" ​ ​ ​ on a bunch of other cards which add combat phases.

but I may be missing something.