Warning - this rambles on for quite a bit, and I've changed the subject line.
No, it's not as simple as you state, although LNA noise figure does matter, it's only significant when you have a small antenna. First of all, when considering any space link budget, we must stop talking about Noise Figure in the overall system. When antenna temperature is anything other than a warm terrestrial 290K it becomes meaningless. A decent antenna looking up at cold sky may have an antenna temperature of 10 - 30K, call it 20K for now. And now LNA noise figure becomes a lot more significant. Eg a 1dB NF LNA, has a noise temperature of 290 * (10^(1/10) - 1) = 75K. Assuming this dominates the complete receive chain, that means a system noise temperature of 75+20 = 95K.
Which all goes to show that LNA performance becomes a lot more critical when receiving WEAK signals from space.
But now consider a situation where a satellite transponder has enough gain that it is radiating a significant amount of it's own receiver noise but no other signals. Lets say it's radiating sufficient noise such that our ground station is seeing that transmitted noise at a level of 5dB above the ground station's own noise level. BUt it is a radiated signal now, and as such cannot be directly added in to the ground stations own noise in any meaningful way. Here, for example, that 5dB increase in our 95K system defined above, 3.16 in linear terms, could be said to correspond to a new receiver noise temperature of 3.16 * 95k = 300K, of which 95K is our own, the rest from the satellite
But if we used a bigger antenna on the ground, and saw a transponder noise level 10dB above Rx noise, that could be said to be 950K by the same argument. Which is absurd - increasing antenna gain does NOT change system noise temperature.
So ... yes, LNA performance does contribute to overall system performance, and more than in dB for dB terms, but ONLY WHEN receiving weak signals from space. A satellite downlink from a linear transponder IS NOT A WEAK SIGNAL if you are using a 'normal' downlink receive antenna, so LNA / LNB performance is not that critical.
I believe, although can't yet prove for myself as I have a slightly blocked view of the satellite, is that a 60cm dish and good LNA results in transponder received noise floor appearing about 5dB above receiver noise. Goonhilly uses a larger dish
What actually IS the weak signal when operating QRP into the satellite is defined by the satellite's antenna gain and noise temperature. Now, a satellite antenna global beam looking at the earth will be seeing warm terrestrial noise, and have a much higher noise temperature - something like 200K used to be taken in my old days working on Inmarsat as there is some attenuation of hot earth and spillover into cold sky - sort of sidelobes working in reverse!
Assume a low power uplink results in a received S/N of 10dB (using a noise bandwidth appropriate to the signal of interest). That S/N will be radiated by the transmitter and can never be bettered, whatever you do to the ground Rx system. Only if you have a very small antenna or poor LNA wil there be significant further degradation.
There are so many interdependent variables in a satellite up and downlink using a bent-pipe transponder that it is only really possible to get exact contributions from any particular part by putting together a spreadsheet containing every single parameter. And unfortunately, for this system, we don't have all the satellite parameters to hand to do this properly. We don't know transponder gain and we can only estimate Rx noise figure / temperature and the Rx and Tx antenna gains.
What makes life even more complicated is when receiving LARGE signals via the satellite. If you have a very small ground station antenna (or poor noise figure) and can't see transponder noise you'd still get them - but now your own Rx performance really is the limiting factor - which is actually my situation at the moment.
I did say it wasn't straightforward !
Goonhilly, with it's 1.3m dish is seeing a transponder noise floor something like 10dB above thermal, so any QRP operation via that is entirely dependent on uplink EIRP and coding efficiency. SO the WebSDR there is an excellent receiver goto when testing QRP uplink operations.
I've rambled on a bit here, but hope you can see that for any typical ground station, unless the operators reduce the transponder gain significantly, anyone with a recommended system of 60cm dish or more with good LNA should be seeing transponder noise. Ground station LNA noise figure does matter, but certainly not in a one-for-one dB related way.