That i am not sure about, i have no ideas what kind of signals wizz thru a HDMI cable, but some of them may short circuit and destroy the camera in worst case.
I would just remove the memory card and play the files on my computer or other devise that have a SD card slot of USB, using the camera itself as a player are not something most people do.
If you want to play on your TV it should also have a USB plug, in that you can put a card reader and then use the player in the TV that's probably a lot more easy to use then what the camera have.
My TV have a little USB - > USB wire permanently connected to i can plug a memory stich or anything with media in it to play it on the TV.
I have some HDMI to mini or micro HDMI adapters i use when i mess with cameras, mostly adjusting focus if i have changed lens, in day to day operations the HDMI port on a camera are not needed, its only if you want to use the camera as a player.