Amplifiers don't put out impedance, they react to impedance. Impedance fluctuates with every movement a voice coil makes and when they're in use, they're in constant motion, so the impedance is constantly changing.
As for "box rise", it doesn't exist. At least, no more so than the phrase "sun warm" exists to describe the effect the sun has on the Earth's surface when it rises. If you were to talk about "sun warm", most people would say DUH of course the sun warms the Earth when it rises. And that's pretty much what engineers think when people say box rise. Because... of course impedance rises when the coil is in motion. And on top of that, it rises whether the driver is in a box or not and it even rises when there is no amplifier connected whatever. That's just what happens and you can't blame it on anything other than physics.
So with that said, if an amp isn't .5Ω stable, you can assume that to mean that it doesn't like impedances below ~1.5Ω... because the people who designed it already know what the amp will actually see when connected to a given load. And they have to know that, otherwise they'd get fired or, go out of business. ;-)
Now... with all that said, just because a manufacturer doesn't say his amp is .5Ω stable, that doesn't mean the amp is not half ohm stable. Manufacturers have a vested interest in not telling people to run their equipment at its limits. Ladder manufacturers will tell you not to climb more than 6' high on their 8 ladders but that doesn't mean you can never climb to 8' on them and it doesn't mean you're certain to fall if you climb to 6'6". It just means they're protecting their interests and that you're responsible for your own safety.
So coming back to your question... yes, your amp will likely see a 1Ω or higher load if you run it at .5Ω. And Jacob Fuller knew that when he didn't tell people his amp could be run at a half ohm.