Is noise figure dependent on input noise power?
To answer your question, Noise Figure is the amount of noise that would be added referenced to the input of the amplifier assuming no prior noise amplification has been provided in a properly matched system. This equates to a change in the SNR of the output relative to the SNR of the input, and the input noise level with no other gain would be typically referred to as the "thermal noise floor".



So given that, and to your example, if the gain of the amplifier was 1 (0 dB) and the noise figure was 5.5 dB, then in this case the signal out would be equal to the signal in (gain = 1) but the noise out would be 5.5 dB higher than the signal in. (and hence if you follow SNR out vs SNR in you see that this would hold).

To further demonstrate, consider if the amplifier had a gain of 10 dB with the same 5.5 dB Noise Figure. Here the signal out would be 10 dB higher than the signal in, but the noise out would be 15.5 dB higher than the noise in.

Now to further demonstrate noise figure, consider the same case with adding a noise free 10 dB gain amplifier in front of our noisy 5.5 dB NF amplifier: At the input to the noisy amp the signal will be 10 dB higher and the noise will be 10 dB higher relative to the thermal noise floor. Our noisy amp adds +5.5 dB of noise relative to the thermal noise floor, so referenced to the noisy amp input according to this noise figure model, in this case, the total noise will be:

$10Log(10^{10/10}+10^{5.5/10}) = 11.32$ dB above the thermal noise floor.

While the signal will be 10 dB above the input signal level at this point.

(Note this isn't the actual level that would be measured at the input of course but is the "input referenced" noise as measured at the output of the amplifier--as the noise is added in the amplification process).

At the output of our noisy amp, due to its +10 dB gain, the signal will be an additional 10 dB higher, as well as the noise, resulting in a final noise output level that is 21.32 dB above the thermal noise floor. The total change in signal level was +20 dB, while the total change in noise level was +21.32 dB. The change is SNR was therefore only 1.32 dB. This is the Cascaded Noise Figure showing how a prior lower noise amplifier can reduce the overall noise figure of the system.  The actual formula for this is given below, but following the details above helps give the background of how this works. The bottom line is that the noise figure is the additional noise that is added referred to the input of the device relative to the thermal noise floor. Increasing signal and noise prior can swamp out this additional added noise later.   

$F_T = F_1 + \frac{F_2-1}{G_1} + \frac{F_3-1}{G_1G_2} ...$ 

Where 

$NF = 10Log_{10}(F)$

and gain in dB = $10Log_{10}(G)$