Is there any danger of damaging yourself or your microwave if you turn it on with nothing in the oven?

I think it could, You can always try if you are curious. Do you have an excess amount of money to use with nothing in it, and a replacement if needed?
You should be safe, Interlocks prevent using with the door open.
I guess you could override the door interlocks, and see what damage occurs.
There is a reason for the interlocks. Safety

Smithy,

There's little danger to your person, provided (as Stratmando mentions) the door interlocks are working correctly.

But you risk damaging the magnetron through standing waves causing it to overheat and burn out. An expensive repair!

Daniel