My question would be, does high end preamp reduce the noise floor in budget microphones?
Depends on which microphones we are talking about. Generally, for most condenser microphones, the answer to that question is no. This is because the microphone's output noise is generally in excess of most preamps' input noise. Those two noise signals sum, but if the mic's noise is far enough above the preamp's noise, then the mic's noise will dominate and the preamp will make little to no difference.
For lower output condenser mics it can make a difference, and of course for any type of dynamic mic a very low noise preamp is critical to obtain the best possible signal-to-noise ratio. But even in the best preamp there are limits; you aren't going to get lower noise than the thermal noise of a 150 ohm resistor (in the case of a ribbon mic, the resistance of the element multiplied by the gain of the transformer), which is -133dBV (or about -137dBA). Nobody achieves that though; the AEA is spec'ed at -134dBA. So if you have a ribbon mic with -57dBV/Pa sensitivity, then the signal to noise ratio isn't going to be better than 77dB, which is equivalent to a 17dBA self-noise rating for a condenser mic.
With that in mind, even if 83dB of gain sounds great, in practice it is not useful. This is because once you raise your noise floor more than 10dB above the noise of the next stage (for most people these days, a converter), you don't get any further benefit from earlier-stage gain. For a typical converter, that noise floor is probably between -90dBV and -100dBV. So there isn't really need for gain in excess of 50dB. It might feel good to record a signal that ends up closer to 0dBFS rather than -20dBFS, but there is no difference in signal to noise in that case.
A few other types of "noise" that aren't noise in a specification: interference and phantom power supply noise. The AEA pre has a really good CMRR spec, so that might result in an audible improvement in a difficult EMI environment. The AEA doesn't have phantom power, but a preamp with a noisy phantom power supply can result in that noise injected into the audio with certain condenser microphones that have not been designed to cope with noisy supplies. It would generally not be noticeable with a dynamic mic, since the CMRR of the amp will cancel the noise in that case.