RE: Flying wing?
Unless it has a symetrical wing or is nearly symetrical I'd say no.
I'm assuming that it's a straight constant chord sort of wing with strip ailerons and the usual flat bottom generic "shoe sole" shaped leading edge and upper shape. So what you're asking about is a plank style flying wing.
For a plank wing to be stable it has to have a positive pitching moment airfoil. And the usual flat bottom trainer wing airfoil is strongly negative pitching.
The way to get around this is to add some upward "reflex" to the strip ailerons. But on a typical trainer the ailerons are not wide enough. And besides, the fixed forward portion of the wing is typically so strongly negative pitching that you would need to double the width of the ailerons and even then use a LOT of up trim. By that time the airfoil is so inefficient that it's like flying with spoilers deployed all the time.
On the other hand if this wing has a symetrical or "semi symetrical" airfoil with zero or very little camber it does not require much reflex to change the airfoil's pitching effect from negative to positive.
So in a way the answer is "it depends".