Yes, Unless They Are Mismanaged...
I think the phrase "The House Always Wins" is more associated with
slots and Table Games... of course the
odds are in their favor, or as have many have said, if the odds were not in their favor, there would be no house! That of course does not mean that someone cannot win on occasion, just that over a large sample size, The House Will Win!
But when it comes to poker, yes there is overhead that has to be covered in providing a game, so that translates into the "Rake"... but unlike slots and table games, there is a skill factor involved. So no, the house does not always win against an individual poker player, it just depends on whether your skill is good enough to beat the rake.
The House (ie - The poker room / site) can also lose by being mismanaged in terms of guarantees offered in games or by owners not running a financially responsible business, or worse, pilfering players deposits...
Best of Luck At The Tables, All!
Teddy