Can excellent tubes transcend modest amps?

I am wondering how far a good but not amazing amp design with decent parts such as Antique Sound Lab AQ1003 DT or a Jolida 302B can be improved by putting top notch NOS tubes? In other words, is it worth buying a used $500 integrated and give it an extreme tube make over for $200-400 rather than buying say a PrimaLuna or Cayin in the $800-900 range with its stock tubes?
My first comment was that the better and more resolving the system, the more the qualities of NOS tubes would be appreciated. NO- They WON'T transform junk, and I fully agree that a well built power supply, quality caps, etc. ARE an absolute must for "high end" reproduction, but: Quality NOS tubes will still take a mediocre amp to higher level, and the differences will not be subtle. Incidently: A high-dollar set of Michelins WILL have more traction, and result in better stability, ride comfort and handling on ANY given car(providing said car didn't already have a better set of tires on it). Will they transform an Impala into a C6? Of course not! They WILL however make an improvement.
So a Cayin 70 0r 88 with a bit of tube upgrade may be the best of both world in the budget category?
A pair of these: (, and NOS TungSol JAN CTL/6SN7GT roundplates or Sylvania JAN/CHS/6sn7W tall bottle tubes from the 40's as drivers in the A-88T would probably satisfy your craving for a taste of the high-end pie(entry level, but solid). That would depend on your SPL needs, and the rest of the source material/system/room combination of course. Personally- I'd use Winged 'C' 6550's(the latest iteration from the St Petersburg factory) as output valves, as I know them to be a very clean tube. Slightly more power with the KT-88's, and you could well be pleased by the stock outputs. You didn't mention your tastes in music, or listening levels. Be certain to buy matched/tested/certified pre-amp grade(very low noise) 6SL7's for the piece. Finding NOS 6SN7 "Grails" that are screened for noise will be tougher, but they shouldn't be in as high a gain stage anyway.
Better tubes make a mediocre amp better but would go so far as transcending it. On the other hand, the are great amps made with so so tubes and still sound great. I would say great amp transcends modest tubes