Yes bleach can help clean a shower head and remove calcium deposits.
Vinegar is also another good way of cleaning a shower head and you can use vinegar and baking soda together as well to clean a shower head.
I've used bleach to clean shower heads and it does work but vinegar and baking soda also work and work sometimes even better at cleaning calcium deposits from your shower head.
You can pour some bleach into a plastic bag and tie it around the shower head and leave it for a few hours or overnight or you can also use some vinegar and baking soda or vinegar by itself in a plastic bag too and tie it to the shower head and leave the bag on the shower head for a few hours to overnight.