iMac 27" Mid 2011 -- fan issues when removing internal HDD?
Will I also run into these issues when I just remove the HDD?


Yes.  

The reason being is because that vintage iMac used a quasi-proprietary drive that had a temp sensor built in.   Remove the drive, you remove the sensor and the fans spin up full speed.

Instead of just removing the drive, add an SSD and use an inline temperature sensor to regain the functionality.