You can drill a backbox lock, but it's not the same as drilling a coin door lock. Rather than drill all the way through, like a coin door lock, you want to drill the tumblers. Use a bit about the size of the key slot. You'll feel each of the tumblers 'give' as the bit cuts through them. Do both sides. Once you think you've drilled enough (you probably haven't), jam a big standard screwdriver in the slot and see if you can turn it. If not, blow out the shavings and drill some more.
It's messy and usually takes a while, but eventually you'll be able to turn the lock. If you have to buy the right size drill bit, buy two as broken bits happen when drilling tumblers.