Yes you can do this but you've put aside a number of issues, besides streaming radio. Your own files, other streaming services, sound quality etc. There are many ways to approach this Erik's rec is certainly valid, being less computer savvy I went with an affordable streaming option the Auralic Aries Mini. Many hear also seem to like the comparably priced Blue Sound Node. Also in terms of sound quality I'll say I noticed a definite jump going from playing files off my laptop or a usb drive plugged into my laptop to a dedicated NAS drive. Also not sure about you but I hate running wires all over the place the wireless nature of my setup works for me. Lots of threads on this stuff here many of them very recent.
Far Cheaper than a $3000 Music Server
Suppose you have a reasonably high-end DAC, such as an MSB Platinum with upgrades that include a re-clocking buffer that makes the jitter of the input digital irrelevant. You would like to use your PC to play streaming from radio stations that otherwise offer only fringe reception for even the most expensive FM tuners. You can do better, but not perfect, only comparable with HD radio which you can't get in a fringe area by taking digital output from your PC to the high-end DAC rather than using the cheaper DAC in any sound card you can buy. The way to do this is to take a USB cable from your PC out to an external converter that changes the digital to toslink or coaxal and conveys it into the DAC. Signstek sells a "Mini USB DAC" that does this. It also has a cheap DAC in it but you will bypass it for the better DAC already in your system. There are other such converters, but this one plugs in without having to put any software in your PC and it is ready to use. You can store music in your PC and play it through your sound system the same way you would use a music server that costs at least one hundred times as much.