It is definitely possible... it is also easy to end up with software synthesizers that use up large chunks of your available CPU power, or even synthesizers that require more CPU than you have available. It is also easy to end up with a beloved software synthesizer that stops working because you updated your computer's OS. I have sound modules from the 1980s that still work exactly as they did almost 40 years ago. I can't say that about software I used in the 1980s.

A lot of modern synthesizers or sound modules are basically just software running on CPUs, DSPs, or even FPGAs.

That is what is used for modern music production in software. It's a somewhat new development and with too many in use at once, you will have to prerender/cache the sound as your computer may not be able to handle it all live.

But previously it was all analogue electronics. Which are extremely difficult to perfectly replicate in software and even models of the same synth would sound slightly different due to manufacturing differences/defects.