I use it all the time. YES it does harden and I wouldn't recommend it on foam to glue them together, plus I have seen deer hair smoke a little from it. I use it for heads. I run a bead of it along the thread and then whip finish.
It is a waterproof superglue and that is all. Hard as nails is a GOOD answer. If you wanna glue foam together get some sprey on glue like 3M (the kind you spray both sides, let it sit for a few then stick together)