It's quite a good question, your "Home Start" cover would apply as you have a non runner, so long as they don't getting running LOL otherwise you willl be stuck.

So long as they recover the car on the lorry I would think it dosen't matter if it's road legal.. It may be worth reading the "Small Print" as it may state in there cover only applies to a road legal car as not sure how the insurance situation would work.

Martin