No, you can't improve the noise performance by adding source resistance. The trap you're falling into is that the "noise figure" improves because the transistor is adding the same noise to a noisier source! This is specmanship not engineering...
One good way of reading the graph is to focus on the "3dB" curve. The importance of this is that "3dB" means doubling the noise power : in other words this is where the transistor generates the same noise power as the source.
So you can see that the transistor is as noisy as the following resistor (i.e. has an "equivalent noise resistance" (ENR) in each case:
- 100 uA : 120 ohms
- 300 uA : 50 ohms
- 1 mA : 35 ohms
- 3 mA : 25 ohms
- 10 mA : 20 ohms
This is what the transistor does, in terms of voltage noise (thermal noise, Johnson noise). Now compare these "noise resistances" with your noise budget and choose your collector current accordingly.
The upper 3dB curve shows the performance limit in terms of shot noise (current noise, where the statistical fluctuations in current flow develop noise voltage across high resistances. Ignore that curve for now by staying well away from it! Just note that you had a high source impedance, that's the curve you'd be looking at instead)
If you need a lower noise resistance, the way to achieve it is to use a transformer ahead of the input, to transform the transistor's noise resistance to match your budget.
EDIT : earlier version didn't take RMS summation of noise sources into account properly.
For example, if you need a 1dB noise figure at 50 ohms, that would imply 0.1x the noise power, or a noise resistance of sqrt((50 + 50*0.1)^2 - 50^2) = 22.9 ohms. The "3dB" curve suggests this is achievable around 10mA collector current, but the "1dB" curve suggests the target is just missed even at the curve's minimum at 6mA. What happens above 6mA is that the upper curve is starting to converge towards the lower, i.e. current is high enough that shot noise must be added into the budget.
A 1:2 transformer will transform your input voltage up 2x, but transform impedances by N^2 or 4x, so making the source impedance appear to the transistor as 200 ohms, demanding a noise resistance of 4 * 22.9 = 91 ohmsto meet the budget. Or alternatively, translating the transistor's 50 ohm noise impedance (at 300 uA) down to 12.5 ohms at the input, comfortably meeting the budget while saving power. Obviously you also have to budget for the transformer's own winding resistances, and design the transformer accordingly.
Impedance transformation is how vacuum tube triodes, with noise impedances like 300 kilohms, can nevertheless provide low-dB noise figures, even for low impedance ribbon microphones.
So if you cannot afford 10mA collector current, you can use a higher ratio transformer to achieve similar results at lower currents and higher ENR. (Don't take this too far; you'll run into the upper shot noise curve!)
One further note: Vce=6V is probably just a convenient place to measure the noise figures. A lower Vce is unlikely to greatly impact the noise. It will impact dynamic range however, because the amplifier will obviously overload at lower voltages...