You could try that - although for the reasons I mentioned above - about ambient noise being the main noise source - it's probably not worth it.
Some months back I had a problem with my Rode NT1. (See
this post ) It showed me that my op-amp circuit was about 3dB worse than Rode's noise figure for the NT1 (which is specified as a pretty low 4.5dB(A) ).
Add another couple of dB on top of that extra 3dB for the OPA Alice configuration and you're still only talking about 10dB(A) or so of self noise.
According to Neumann that's still considered 'extremely low noise'..... As they describe on
this page the ambient noise will still be the dominant noise source.