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.

A simpler yet still pretty effective approach is to install macs Fan Control https://www.crystalidea.com/macs-fan-control in there you can easily set you fan speed to be controlled by any other sensor (just pick one that is close enough to the main source of heat) voila, fan speed down, no additional hardware tinkering and works very nice with SSD as well