During certification testing with jet transport aircraft, go-arounds with spoilers extended are done, and indeed with one type, the Lockheed L1011, it works just fine.
Is the climb gradient affected?
Of course it is, as you would expect.
Another type that does not automatically retract spoilers in the event of a go-around is the original swept-wing transport type...Boeing 707.
Spoilers are all manual operation on this type.
Now, having said this, going around once the airplane is on the runway, spoilers have been extended and possibly reverse selected is a very rare event, and sometimes it doesn't work out for the best.
An AA B727 at STT comes to mind.