Yes, EXCEPT the quad ESC will have no Battery Eliminator Circuit (BEC) or low battery voltage protection, so you would need to have a separate BEC to power the receiver and servos. You would also have to be careful not to over discharge your lipo vs simply spending $15 on a fixed wing ESC like a Hobbywing Skywalker or Hobbyking one, both of which have 3A bec.
Simple answer is YES!
First thing to do is make sure that the ESC has a BEC built in or you add an external.
You may also have to change the programming in the ESC, depending on how the quad was set up. (temperature safety, brake, etc...)
Yes, it will, but don't overload it too much. Quad ESCs are used to being in strong airflow and rarely have much in the way of heatsinks to make them light. Plane ESCs usually include both a aluminium heatsink and a BEC to provide a regulated 5v feed of power for your receiver and servos. Quad ESCs usually don't come with a BEC.
As stated in the thread above both the ESC and the motor should be fully functional, all of the smaller FT power Packs use quad motors.
Also correct is that you run the risk of killing your batteries with the quad ESC because it does not have a low voltager shutoff.
If you're computer Savvy you should be able to reflash most ESCs to activate that cutoff and possibly even the BEC circuit if included but at that point you're probably going to have plenty of ESCs lying around and won't need to swap parts between aircraft.
If your ESC doesn't have a BEC circuit your quad will usually have one included in the Power distribution board, so you could swap that in as well, but unless the quad is beyond repair it might not be worth the hassle instead of getting a new set.
I did this with some old unused multishot ESC's and used Racerstar "F-pack" motor, and a 4ch FrSky RX. Just had to buy a 5v BEC. It works perfectly on my Arrow. I dont see any reason why not run this way if you have the parts laying around!! It just will require a but of custom wiring which should be no problem.
I have seen various mAh allotments for the BEC, but I went with ~500mAh per servo rule.