Can I run a 120volt 120 watt Hard Wire towel rack connection to an existing GFCI with-in the same bathroom ?
Yes, the towel rack can be on a circuit with receptacles
Because it will amount to less than 50% of total circuit capacity. You cannot have receptacles on a circuit where more than half is provisioned (reserved) for fixed loads.
This heater has a nameplate of 120 watts, which is 1 amps. Now, normally a heater is defined as a continuous load. So we must provision 125% of that, or 150 watts (1.25 amps).*
The capacity of a 15A circuit is 1800W (half is 900W). The capacity of a 20A circuit is 2400W (half is 1200W). Even with the 125% derate, this device is nowhere near half.
Therefore it can share the circuit with other fixed loads and receptacles, as long as all the fixed loads together total less than half circuit capacity.
* This 125% is exactly the same thing as the "80% derate" you hear about for continuous loads, just we're applying it to the load instead of the circuit. We must do it this way because it would mix with other loads that are not continuous.
I have this exact setup at my house. I did pull a second circuit after my wife tripped the breaker a few times, if you turn the bar off there will be no problems (mine has a switch on the bottom of one of the uprights) but with the rack on and a hair dryer it would trip the breaker when she would forget to turn it off. Warm towels are so nice getting out of the shower.