If by "this version" you mean FSO, yeah. Freespace Open does support playing with mouse, I do it all the time.
That said you need to understand that Freespace Open is a large partial redesign and improvement of the game engine, and it comes with new binaries and such. In order to install FSO (preferably via
Knossos mod launcher and manager), you don't need to have the retail FS2 actually working or to buy the GoG version. Knossos requires only to have the nine .vp files present in retail FS2 in order to install FSO.
If you can install FS2 from your disks but not run it, Knossos should locate the needed files automatically.
If you can't install FS2 from the disks for some reason, you could also just open up the disks and copy over the nine .vp files from them to somewhere and then point Knossos to that directory.