Yes probably. Cold slows everything down. But I don't know which slows down more.
Also, having dug a bit deeper, the bacteria also break down the glutin network. So "overfermenting" is still also a way to flatten your bread. It's not just protease activity.
I just did 100% spelt loaves, using a much larger 15% starter innoculation so it would happen faster (to ensure protease isn't the problem) and at about 150% rise (alloquat jar test) I shaped and did a very short 30 minute proof before baking, no refrigration. The first loaf was overproofed already, the second loaf (35 minutes later) was flat (but airy enough to be totally edible, just flat with no ears).
Even though spelt has more protein than wheat, I can't get a good well developed strong dough with spelt. The dough is just very soft. Quite a tricky flour.
Next time I'll just proof and bake sooner, and also lower the hydration (I got a tip that spelt doesn't work at high hydrations like wheat does).