"could I do this legally". I would like to advertise my business as being *free *if they agree to the program being on their computer.
As long as there is no deception, you can operate a miner on someone else's hardware, legally.
I hope to see this as a long term thing so I can stack up the number of computers mining for me.
The problem is that CPU mining is unprofitable and not worth your time. And few people have GPUs worthy for Bitcoin mining. Even then, GPU mining is soon likely to be unprofitable (when considering the cost of electricity and assuming the exchange rate is at current levels or below) and is not worth your time.
Mining in the manner you are suggesting will only cause frustration to those you've suckered into letting you proceed. If you rely on those customers for service revenue, there probably are better ideas for bringing in some income.
You might even consider some of these suggestions:
Where can I find a Bitcoin-related job? -
http://bitcoin.stackexchange.com/a/4867/153
