Yes, there would be a sonic advantage. But is it worth to you? I don't know, and I suggest you think that through.
Here are some points to try and help you in that process.
Is this your only source? Maybe you like spinning discs, or a turntable better, and this is for non-critical listening. In that case I would leave it as is, or look into your DAC chain. BTW, I'm not familiar with Macs beyond iPad/iPhone, so can't say much about iTunes+Pure Music. I do read often Mac user like iTunes with Audionirvana+, FWIW.
A computer is a noisy environment and building a dedicated server can be done addressing this issue to varying degrees.
Power supply: Replacing a switching mode power supply is one step, but then there are folks taking that to the extreme of having separate supplies for the OS SSD, for the music HDD, for the mobo, and lately some are experimenting with supplying direct to the RAM modules. As you go deeper, there is a benefit, but again, is it worth it to you? BTW, the above is not expensive, but it can become cumbersome.
Internal computer processes: computers run a number of general processes that are not needed for audio, and many motherboards come with many features that we don't really need for audio that forces some process to be running. So one approach here is using a operating system optimizer, such as AudioPhil's Optimizer for Windows Server 2012, to turn off all unneeded processes.
Using a SSD for the operating system with a separate power supply and an upgraded SATA cable is said to improve sound significantly. Using an audiograde USB card is also a big improvement.
Getting rid of motors is also said to improve sound. There are passive cooled cases so you can avoid a fan, and if budget permits use a sSD for the music, but separate from OS.
I, myself, am in the middle of this journey. I used to be 100% spinning discs. Then tried a Squeezebox Touch and got hooked with the convenience. Later tried a laptop with Windows and liked it better, and started learning about servers. For the record, I'm not the type to endlessly tweak software - I'd rather listen to music in the limited free time I have at home. I'm now building a purpose built server incorporating many of the above. I will be incorporating them one at a time to assess the sonic impact.
Sorry for the long message. I wanted to put into perspective what I stated at the onset. I hope it helps.