Short answer is yes, you can probably improve it fairly well.
My first attempt was to use a denoise plugin. Izotope RX will learn what noise sounds like and I picked a section which was just violin, used that as the sample, then played with amounts and ratios and all sorts of junk. Second, you can EQ some stuff off of the top end (say, 4-5db) above about 4khz to try and eliminate as much of the harmonic's first.
The downside is time. I think it would take about 30 hrs of work to fix this, most of it's finding the right settings, and then about 10hrs of system processing time (whether all at once in batch mode, or in segments).
I've attached the solo results and the original segment I used. Again, this was the 30 seconds quick and dirty, it could be improved more with some tweaking of settings. Rename the files to flacs (only shn's can be attached).