No, it doesn't

You need to thinker with external software... i think the D3Dwrapper which is used for 3d accelleration under modern Windows OS has some kind of basic joystick emulation, but it's probably better to install vJoy, to have a universal virtual joystick device, and try to do some configuration there.

It should give something more or less usable, even if maybe not ideal

The lack of mouse support for X-Wing Alliance is weird. I remember playing a demo of it on a demo disc in 1999 and the demo had mouse support.

It was probably the demo for one of the earlier DOS games, X-wing and Tie Fighter had mouse support in their DOS versions, which was removed in the windows remakes (along as some other stuff that makes them the worst versions).
X-wing vs Tie Fighter never had mouse support even in the demo, and the same for XWA.
Source: I played the demos for both of them for months before being able to get the full games because I lived on a small island before buying stuff on the internet was a thing, so it was either waiting for the local PC shop to get a copy after having ordered it or just snag a copy while travelling to the mainland.