Hey...
Yeah, it will install fine without entering any activation key. You can only use the operating system for 90 days I believe until it will become totally shut down. You'd have to run a command before each 30 days is up, 2 times, to get the full 90 days. If not, it will only last 30.
I'd recommend not to install until you figure out what you're going to do about the key. Perhaps if you have a receipt Microsoft may issue a new key to you. I can't say for sure because I'm not an employee of theirs.