Do vacuum tube test values reflect sound quality?

@lewm  Thank you.

So, would it be better if the 3000 and 2750 values were more closely matched?  The two tubes match each other closely which I assume is good. 

Have you heard differences between tube brands thru THAT unit?

I would listen to the ones I bought, AFTER I break them in for 60 hours by simply leaving the unit on, no signal required, and if they sound great, expect many years of life.

IF they don't sound great, try a different tube not the same one, no matter what it measures.

Sound good, but not better than prior good ones, there's your 'never without music spares', find some that you prefer some day. 

Keep in mind, each time we push pins in a socket; rotate a dial; move a switch on a tube tester, it's similar but can be slightly/perceptibly different; and published numbers from two separate testers are not scientifically exact.

If you had your own tester, then you could test them when received, and every 6 months, keep a chart, have confidence in your tubes when problems occur. 

@elliottbnewcombjr I've tried several different input tubes as well as output tubes.  I can hear noticeable differences.  I'm pretty set on Telefunken ECC801S for input tubes.  Siemens ECC801S being a close second.  

I hadn't tried very many different output tubes until recently.  I now have a couple of pairs that work well.  I just thought I'd try something different for grins.   

These days, for the exotic types and brands you mention (Siemens and TFK), I’d hazard a guess that there are more fakes than real ones on the market. I’d stay away from eBay as a source for such tubes. Most reputable dealers don’t pretend to have such tubes to sell. I assume you know that “ECC801”indicates a selected ECC81, even more rare than the run of the mill version of Siemens or TFK. What few exotic small signal triodes that I own I bought in the 1970s, so I know they are for real at least. However, maybe you are an expert in examining these tubes to prove to yourself that they are what they say they are. I certainly am not, even after 45 years in this hobby. To the question you did ask, yes I think 3000 and 2750 are sufficiently well matched sections.

As lewn stated, one cannot tell by numbers what a tube will sound like.  The sound will be determined by the particular amp and the particular brand and construction of the tube for any given type.  Depending on the application, a tube can test quite poor, but can sound perfectly good in an amp that does not push the tube very hard.  It may also sound like a sibling tube even if the two test very differently.

I notice you are using very expensive Telefunken ECC801S input tubes.  I hope you got it from reliable sources because the Chinese have become quite good at making fakes, including fakes with the raised Telefunken diamond in the bottom of the glass envelope.  I got my pair for my phono stage a long time ago, and even then I worried about fakes.  The boxes they came in looked very clean and bright, which worried me until I tried to open them and they started to fall apart from age.  That was a good sign to me.