While this would not be the most efficient allocation of resources, yes, a better DAC will make a noticeable improvement in even a quite modest system.
At the Washington DC area Capitalfest audio show, a few years ago, one of the best sounding rooms had a low-budget set of components on display. The speakers were ProAc Tablettes, and the amp was an integrated tube amp from Synthesis. This seemingly modest system was putting out beautiful music. The source, I believe, was CD quality files on a laptop. Hidden from view was the DAC, which was an Audio Note DAC 5 which costs may multiples of the combined value of the rest of the system. I think the point was to show that even a set of small speakers and a fairly low-powered tube amp can be really capable, but, it also showed off what the DAC 5 can do.