Not shutting down properly can have consequences.
Although I've never done this myself, I'm quite sure that if you don't shut down in the correct fashion, that it can cause issues on next boot up.
Ronin, you are right. Not shutting the server down in a proper fashion can corrupt files on the hard drive. The only time I recommend pushing the power button or cycling the power on your remote reboot port. Is when the server is not responding to any other commands.