At Lowe's for $7 you can buy this adhesive glue in a spray can.   Loctite makes it and the can says it's good for "foam".    I was looking at it because I broke one of my ICF panels during shipping.   I thought, hey what if I used this glue to bond together the blocks as I make the structure.   It would make the structure stronger and prevent blow outs.   Is that a good idea or a hairbrained idea?

Just screw a 1 x 6 on each side of the wall over lapping the damage to a couple of sound webs. Save the broken panel for near the top where there is less pressure.

You don't really need to buy a special glue. The spray foam in a can that you use to seal holes, cracks and penetrations can be used to "glue" blocks together if you wish. For a broken block, I'd always use mechanical reinforcing like FBBP notes, above.

I used ARXX blocks and a properly built and filled form structure won't need you to glue the blocks together to prevent blowouts.

If you need to repair a piece of foam, you can use Titebond II wood glue also. It makes a strong bond with EPS foam and is probably much less expensive than that spray glue for the amount of coverage you get. I would still back up the repaired area with some wood blocking screwed to the ties during the pour.

Unless the ICF manufacturer recommends glueing all courses of foam together, I wouldn't do it. Not glueing the courses together allows air to escape between those joints during the pour which might help eliminate/reduce air pockets in your wall.

The ICF I am looking to use specifically says don't add the glue because it interferes with the block connection formations. That makes sense as you are taking something that is supposed to be a tight fit and inserting something in between. Only place they recommend adding the spray foam is for the first course to connect to the footing better.

If the broken block is on the top or second from top level and you have some mechanical bracing (e.g. like mentioned above), it should be okay.