If you could get a round of .45 auto (.45acp) into a pistol chambered for .45GAP, it would not go into battery. It is too long for the .45GAP magazine, meaning the only way would be to drop one through the ejection port directly into the chamber.
It will not fit well enough to fire.
HOWEVER...
A .45GAP would fit into the magazine of say a Glock 21 in .45AUTO (.45acp). It would strip out of the magazine and chamber. The .45GAP would most likely be held against the bolt face by the extractor. When the trigger was pressed it would fire and most likely eject. Nothing would blow up.
I am making an educated guess. I have in fact fired a bunch of .40S&W through a G20 10mm. It fired, functioned, and was accurate. I did it to see if in an EMERGENCY I could fire .40 S&W out of my 10mm Glock. I have since bought a .40 S&W barrel and a .357SIG barrel for the G20.
I have little doubt the .45GAP would work the same through my G21 .45AUTO.
CAVEAT
AS A FACTORY CERTIFIED GLOCK ARMORER I AM STRONGLY RECOMMENDING AGAINST FIRING .40 S&W OUT OF A 10MM, OR A .45GAP OUT OF A .45AUTO!!!