It is very unlikely to cause problems.
Someone I know has a gaming laptop they leave plugged in 24/7 and are usually playing games on it, and the battery is still working fine.
I run a teamspeak server on a netbook, plugged in and running for a year and a half with no issues. However, the loss of battery life is hard to know because the battery was already useless (it was being given away for free to a friend).
I think I feel confident in saying it will be safe and nothing will go wrong, and that for the first couple of years you will not notice a considerable drop in battery performance.