Hi, I plan to purchase a water heater without pump and then install an additional shower head to it.

The default shower head i will still use it but at the same time i wish to have a rain shower head also. Since the default did not come with the rain shower head, so i will purchase 1 from Mr. DIY and install it to the water heater.

May i know is this doable? Is there any problem if i do it like this?

Better at least to buy water heater with pump, otherwise install pump after water tank.
Even I installed water tank with pump in 1st floor bathroom for my landed unit, the rain shower still not optimized as expectation.