In playmoney tournaments; No.
Computer support for move calculation is not allowed. Opening books and opening databases may be used.
In playmoney games we want to match with each other using our own chess skills.
In real money tournaments: Yes.
First we want to have top-quality games. On the other hand it is not possible to check that everyone is abiding by not using computer support. Some chess servers are claiming to be able checking computer support, but this is unverifiable.
But we offer game types in which computer support is not possible! For example in Dark Chess a computer programm cannot supply a lot of support.
For each player only its own pieces and the squares to be reached in the next move are visible. Additonally each player can see the squares in front of its pawns: The sqare directly in front and both diagonal in front. The opponent's king has to be captured. Checkmate doesn't terminate the game immediately. The king must not avoid check.
Because of ignorance of the computer program about opponent's pieces positions, there is no support possible.