It's just overkill basically. And how many you can connect depends on the wall wart rating (i.e., amps it can output) and the draw of your LEDs (10-20mA is common I think).
It SHOULDN'T be an issue driving the 2 coin doors from a wall wart, no matter what.
And the burn out thing - just read up on it. Some PSU's are made to have a draw on them and if you short it out it can overheat/burn out quickly. Also, you're going to be wasting a ton of electricity just to get a 5V line.