No, but if you fix one (or constrain it to a narrow range) then specifying the ratio is equivalent to specifying the absolute amount of the other.
...but I am curious about ratios, especially as they relate to taste.
I am absolutely for that. If you want to record ratios and then try to correlate ratios to some thing perceived in the beer then you certainly should do that. I'll note, as I usually do when this subject comes up, that the chloride:sulfate ratio seems to have arisen from a chapter in the second edition of Brewing Handbook where a couple of papers were referenced one of which said that in one panel test preference seemed to be based on the ratio rather than the absolute amounts of chloride and sulfate.
My spreadsheet calculates chloride to sulfate ratio (but admittedly I never look at it because....
Personally I add just a small amount of CaCl to my water and have great conversions and beers that taste like I intend them to taste typically.
... I do the same thing with the exception that I RO the water first to get all the sulfate out. IOW I much prefer low sulfate beers and am of the opinion that the proper sulfate to chloride ratio is 0. Perhaps this colors my thinking on the subject.