It should be usable - if you go with keeping the foam in the boot, simply get yourself some form of AA/RAC/Green flag recovery cover and if it doesn't work, get the car recovered.
I know I wasn't keen on the standard Vauxhall tyre gunk kit on my last car (Astra VXR) so I bought a spare and all the fittings for the boot but if space is at a premium it sounds a bit like a good plan for you.