Antenna position/orientation, "gain" and the variability of RF noise makes such comparisons challenging, to say the least. Without an anechoic chamber, the basic way to measure internal noise is to substitute an inductor equal in value to the loop (inductance and resistance) and then enclose the amp in a RF-tight box, that may have to also be grounded, depending.
Hi there, let me start by saying that, willing to properly characterize a preamp, the approach you describe is totally correct, on the other hand, for a coarse evaluation of the noise floor, using an SDR and an antenna switch, to compare a given preamplified antenna with a know one will at least give you an idea of the noise floor of the preamp, since the band conditions won't change in the seconds needed to switch between an antenna and another one
That said, while the TL592 used in the MLA-30 isn't exactly a quiet amplifier, it isn't the real issue with that antenna; most of the MLA-30 noise comes from the voltage multiplier IC used in the original BIAS-T circuit, by either modding it (or replacing the whole unit); as an example, I ran a simple test tuning to the Shannon VolMet and then swapping back and forth the standard BIAS-T and another one from a miniwhip, with the original BIAS-T, the VolMet signal got lost in the noise, with the other one, the VolMet signal was readable although with a bit more noise than the one I got using my "LLD" (linear loaded dipole) antenna, but that was expected since the MLA has a preamp (and then being wideband [untuned], it's also subject to IMD in case of strong nearby signals)
What I can say is that, by replacing the BIAS-T unit (or modding it), replacing the stock RG-174 coax with better one and adjusting (lowering) the preamp gain trimmer, the performance of the MLA-30 improves quite a bit, and while it won't become a skyloop or the like, the improvement is particularly noticeable with weaker signals, then by the way, there's little one can do with propagation, but at least, after the modifications, the antenna will contribute much less to the noise level
and, all in all, it's all about setting the S/N ratio, not about gain, that's also why I prefer using passive antennas, but I was curious to try the MLA-30 so here I am