I will assume you're asking about synthesis/simulation, and not just making a digital recording and playing that back. Most people can distinguish between recorded sound and being in the same space as a real live instrument, the sound is being created by different mechanisms, sort of like comparing 2D with 3D.
For synthesis, if somebody did enough research, analysis and mathematics, there's no reason why they couldn't create a dedicated simulation of any instrument that didn't use real audio samples.
Reproduction of the sound is not a challenge for the computer, or the software, the challenge is determining the mathematics required to generate the sounds.
Some instruments will need a handful of parameters to generate a convincing tone, other instruments may need significantly more parameters.
Some of those parameters will be fixed because they are connected to the style or state of instrument being simulated, other parameters will be variable because they are determined by the way the instrument is being played.
So I think yes, software can produce a convincing digital reproduction of the sound of any instrument, indistinguishable from a digital capture, if only we solved the problem of how to actually do that.
None of the images in this page (https://www.flickr.com/photos/bbb3viz/) are photographs, they're all generated by a 3D rendering engine. If software can take a 3D model of a landscape and produce photo-realistic images. Then yes, software can absolutely take a model of a musical instrument, and produce the equivalent audio-realism.
We just need to learn how to model them. Something I wouldn't mind experimenting with myself, if only I had the time. :(
As for actually performing that instrument in a way a human would, well that's a whole new level. One step at a time, eh?