Yes, you can (there is a spare SATA3 port in your iMac) and should do it.
Search around the forums and net for what cables etc. you need in addition to the drive with your specific model. I don't know for sure.
While you're at it, you might also want to swap your internal HDD with something bigger (if you don't have the 2TB drive anyway).
You need an Apple replacement hard drive on the 3.5" interface for that iMac, otherwise the fans run all out all the time. There is a second 6GB/s interface, but, if it's a 21.5" model there is no space to mount the SSD without removing the optical drive. On the 27" model, there is space for a bracket for an SSD or to fit one behind the optical drive.
If you still have Apple Warranty or AppleCare you have to have it done by an AASP or void your coverage on the whole machine.
Can somebody clarify this? This would suggest I don't need to spend £30 on an Optibay enclosure for switching my HDD with an SSD (and putting the original SSD in this second position)
Actually, I'm sorry, in the 2011 21.5-inch iMac, there is space for an SSD behind the optical drive, I was confusing it with the 2010.
Yeah it was regarding the space, I'll still need an optibay kit though right? 2011 21.5"
No, you don't need the optibay kit, you need a bracket (Apple) or double sided tape (third party). With the 2011 21.5-inch, you can fit an SSD behind the optical drive and use the second 6GB/s drive interface on the rear of the logic board. All you need (if you already have the tools) is the SATA power cable and SATA data cable -- and an SSD, of course!
Cheers! That's where the confusion came in from your earlier! Can you link me to the bracket I need? Would be appreciated!
I'm not aware of any third party brackets, only the authentic Apple one, which you would have to have installed by an AASP (about an hour to an hour and a half service), otherwise, most third party solutions (iFixit, OWC), use double sided tape to adhere the SSD to the back of the optical drive.