I'm working on a graduate level research project, during my undergrad, concerning yeast genetics in budding yeast, and neither myself nor my faculty advisor are able to answer a specific question when it comes to preparing yeast growth media. The question is: will caramelization of dextrose in solid media have a large or significant impact on the growth of budding yeast on the plates?

Relative to what? The vast majority of labs are autoclaving glucose in the broth so there is probably not a fundamental issue. And I am not even sure that at the regular parameters for autoclaving (121C, 15-25 min) significant caramellization occurs. Of course one could just test it with sterile filtered glucose solution instead, but I would be surprised that on plate you will spot a lot of differences (maybe more so in liquid).

My apologies, relative to growth of budding yeast on plates that had 20% pre-sterilized (filter sterilized) dextrose added to the media following standard autoclaving. The color of the media was markedly different from other solid medias prepared; this media had a dark caramel coloration to it.

Ah yes, if the color is really dark it is possible that the temp in your bottle is getting a few degrees higher (IIRC autoclaving glucose solution for 30 mins at 125+ caused strong discoloration, whereas at lower themp and times it was much less apparent or absent). However, if that happens it is probably a good idea to filter it. That being said, yeast (and certain less finicky bacteria) appear to grow OK on plates even when caramellization occurs (though it may depend on degree which is a bit hard to compare, of course). and colonies did not appear to be very different.

But if you do test growth parameters or for more defined experiments you certainly should eliminate those variables. In addition I should note that sugars can undergo the Maillard reaction with amine groups if present in the media during autoclaving. Again, if precise growth parameters are needed, addition post-autoclaving would be wise.