The Gamecube controller data signal is pulled up with a quite low resistor (around 700 ohms) so it's quite strong and electromagnetic noise shouldn't be able to change it's status.
So no, you don't need it.
You can't remove the pull-up resistors for the controller data line. It's an open-collector protocol (just like the i2c) so the two systems (i.e. the gamecube/wii and the controller itself) can only pull down the data line and to set it high they just "leave it" as it is and let the pull-up resistor do its job.
The resistor is not there to protect from noise, it's there because it is needed for the communication to work properly