You can for a few minutes, more then 4 minutes I've read will affect the culture and can kill them all. I don't use the fridge myself. I just tap the sides of the cup to get them off the lid and pour them direct into my mantises tanks using a feeding hole and a funnel.
All three varieties of flies I have actually seem to have wings, they just can't use them and are flightless. Some sellers confuse the words wingless and flightless, but means about the same thing - that they can't fly.
They can however jump and glide some, with some unavoidable escapees, but they die off quick if they do. Only other thing to point out is any uneaten flies can escape from nearly all mantis tanks - as even the larger Hydei can easily squeeze through the common sized screen mesh.