alvays said:
Will the thermal noise still exists or not?
Yes, thermal noise is present irrespective of the current in or voltage on the resistor.
The thermal noise (power spectral density - i.e. power per Hz of frequency bandwidth) is given by: S=4kTR, so there is no current of voltage entering this formula.
Some other noise mechanisms do depend on current, for example - generation-recombination noise, shot noise, etc.
A more interesting question is - does thermal noise affect the voltage noise on a capacitor?