Actually, it would. You are right that antenna gain and amplifier gain are not the same. Antenna doesn't add any power to signal like the amplifier do, but in this case (reception antenna) antenna is able to receive twice as much power than it did before, while the intensity of EM field at reception point remained unchanged - it receives from one direction more than from another. And that is the reason why we use dBi, as a unit for this type of gain, simply meaning dB over Isotropic radiator.
So your noise parameters stayed unchanged and you have 3 dB stronger signal behind the antenna.