If you were to pump it full and the foam was still liquid and you put the butt plate on then yes you could possibly crack it if it builds enough pressure if there are flaws in the stock or rip the screws out. it depends on the area and the pressure the foam exerts. . The foam expands a good bit so you could fill it a quarter of the way and let it set then top up and see what it goes to .add a little at a time.
and don't try and clean spills while its still liquid . you will be there all day and get it everywhere .
I know they use it in packing of fragile items but that would be a measured amount in the bag before sealing the boxes up. we used to get cylinder heads sent in boxes that used the expanding foam to protect the contents .