Do vacuum tube test values reflect sound quality?

My experience is nope…testing or matching seems to have minimal impact on SQ especially with preamp tubes.Triodes that are unbalanced sound just as good as long as one side tests strong.  Matching and gain balance on output tubes does matter more.  I have a tube tester that is very helpful for comparing tubes and validating whether a tube is good.  Just my humble experience on my system…

I do hope you scored genuine Telefunken 803S tubes.  These days, they sell for up to $2,000 a pair.  The fakers have become increasingly sophisticated.  They use to offer their fakes at a price so low as to tempt even the wary.  These days, many of the fakes are being sold at the going rate of genuine articles which makes it harder to distinguish real and fake offers. 

With things like rare Western Electric transformers, the fakes use to be in too good condition visually to be realistic.  These days, the outer cases are rusted a bit to look old, but often the Western Electric decal is left in nice condition to tempt collectors.  A local builder who buys such parts on line prefers to buy such parts from sellers from Japan.  

"Triodes that are unbalanced sound just as good as long as one side tests strong." That’s true, IF the gain circuit is single-ended as opposed to balanced, and if the section with high transconductance is the one you are using. This is often how tubes become unbalanced; they have been used in a single-ended circuit which only requires one of the two sections where the other section (of a dual section triode) is not doing anything. Some canny manufacturers of SE preamps build their units so that one channel uses section 1 of a dual triode, and the other channel uses only section 2 of the same type dual triode. (Two tubes, one for each channel.) That way, when the tubes become worn, you can swap them from one side to the other of the stereo circuit and in essence you have new tubes. Balanced sections is much more important for a balanced circuit. Also, transconductance is not necessarily a correlate of "gain". Depends on the circuit and the tube. For example, a 12AX7 has highest gain among typical dual triodes, It is commonly used at the input of MM phono stages, because it has highest mu. Mu is equal to Gm*RP (transconductance X plate resistance), and the 12AX7 has very high plate resistance but relatively low Gm. Mu is a better correlate of gain. Gm is more a correlate of how the tube handles current.

@larryi They are ECC 801S.  Clearly labeled with the Telefunken logo.  I assume they are legit, but they aren't the $2000 pair that you mentioned.