Not for transactions which do not belong to them, no. They can refuse to mine any transactions they don't want to, but the transaction they don't mine remain perfectly valid and as soon as the 51% attack ends those transactions can be mined as normal.

They can double spend their own coins only. For example, the 51% attacker might make a transaction paying you 100 BTC. You wait for 6 or 10 or 20 confirmations, and then hand over whatever expensive goods you were selling. The 51% attacker can then mine an alternate chain to replace the last 20 blocks and include in that chain a transaction which sends the same 100 BTC back to one of their own addresses. They have double spent their own coins. They cannot do this for anyone else's coins, since having 51% of the hashrate does not give them any special ability to forge your private keys, break ECDSA, or force nodes to accept invalid signatures.