Teraflame,
I'm going to provide some background, and then try to answer your question at the end. I'll say right now that it is at best 'maybe' - but hopefully I can explain why this is true and help you figure out if a DAC would help you.
I have a similar problem on my PC, using a P6T (LGA1366) motherboard. That you only get the weird noise when 'doing something' should be a blessing, as I get noise all the time. The suggestion that I hear most often is that periodic noise results from electromagnetic interference that is generated by the CPU switching from a low-power power-saving state to an active state as a result of actions taken by the user. In contrast, consistent noise can be the result of any host of issues, not limited to but including interference from video cards, other PCI cards, the PSU itself (corsairs are supposed to be particularly bad, but I am not familiar with the physics to back up that assertion), and a host of other problems.
Since most people don't have extra components available to A/B with, it can be difficult to isolate the specific issue. Ideally, one would swap out each component in turn and listen for the elimination of the problem. Since this isn't feasible, the typical recommendations are somewhat haphazard, but here they are:
First, if your computer has multiple audio jacks, try each of them.
Second, if you have any sort of USB audio device, try plugging them into each USB port and see if one reduces or eliminates the noise. This needn't be headphones, speakers will work too. Just turn the volume up with no music on and listen for digital noise. Try all ports, even ones in peripherals like monitors or keyboards.
Third, though less likely, is try the S/PDIF jack if your computer has them.
From what I have heard, most people have better experience with jacks in the back of the computer instead of on the front face of the case. This is most likely because those jacks interface more directly with the motherboard and have shorter distances to travel over which interference is possible.
The importance of this background is that if there is interference that is introducing noise between your motherboard and the USB/audio outputs, then purchasing an external DAC will not solve your problems because you would just plug it into a noisy input. However, if you have a way of testing your various USB or S/PDIF connectors and can isolate one that has little/no noise, then purchasing a USB or S/PDIF based DAC would allow you to make use of that connector.
For me, I discovered that the USB ports in my monitors have a very low digital noise floor. The one with a HDMI connector works better than the one with DVI, though I am not sure if that is causative or correlative. I suspect this is because these monitors have their own power source, but again I can't be sure. I connected my Pico DAC to a USB port on the monitor and mostly 'solved' the problem. A corollary to this is that one might have more success using a DAC with its own power source, but again, I don't have the sample size to make statistically valid conclusions about whether or not this actually helps, so take these observations as anecdotal evidence at best.
The take-home message here though is that when you are building your next computer you should keep in mind that various components will produce noise and interference, and build accordingly
In your situation my suggestion would be to:
1. Find a USB audio device, or buy one that you can return and test every available output. Do the same with S/PDIF if you have it
2. If you have a low-noise port, find a cheap DAC that you can return, and test the output with it.
3. If it works, then consider what type of DAC you actually want to purchase to make use of the port.
Hope this is helpful.
