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?
I will add my voice to the chorus of answers above. The answer is NO! The sound from your amp is the sum of its parts. I think tube rolling has acquired prominence because it is the easiest part to tweak. After all, you're not going to be changing the output transformer in a hurry, are you?
I agree with the posts above which say that good tubes will make an improvement, but, a better overall quality of the amp will make the superior quality of better tubes even more evident. To me, the biggest determinant of quality is the output transformer, a part which also happens to be the most expensive.

Any particular preference would depend on a variety of factors, such as personal preference, system matching, etc., so experimentation is the only reliable approach to finding the right tubes. It could be NOS, it could be new tubes, it could be "cheap" tubes that will float your boat. It is hard to generalize.

In my system, I generally favor older tubes to current production, but, there are some current production tubes that are very good too. For example,I like EML meshplate 2a3 triode output tubes, but, they seem to be reliable only in amps that run them gently. Small signal tubes have even more distinct personality in my amps; I just happen to favor Tungsol roundplate 6SN7s and Telefunken ECC803S (apparently others like these too, as they are very pricey).
While I agree with a "no, not in general", I have a first-hand experience with doing exacting that: spend almost as much in tube upgrade as in the original price of the equipment. I bought a Yaqin MS12-B preamp for $200 and while decent with stock tubes, I felt the urge to upgrade to Mullard Platinum and other goodies for about $150. Result: spectacular, both as a phono and a line stage, truly mesmerizing and competing-kicking ass with some well-regarded preamp costing up to 5 times my total final cost which are noisier when they are not inferior sounding to mine.
I may be late with this response but here goes. I have or have had the Cayin A88t and the following pairs of driver tubes:
Ken Rad VT-231 (sold and looking for a nos pair)
Sylvania 6sn7w tall bottles
Sylvania 6sn7w short bottles
Sylvania VT-231 (three hole plate)
Sylvania 6sn7 (three hold plate)
Sylvania 6sn7 (two hole plate)
Marconi 6sn7 (three hole plate)
Brimar CV1985
Ratheon 6sn7 JAN
Re-issue Tung Sol
Stock of course (i believe these are eh)

The differences between each are as distinct as if you were listening to different amps (albiet the sylvanias which have a characteristic sound). Even the gain tubes make a big difference. There are brilliant new manufacture 6dj8 family and 12AXT family tubes but in this category I have yet to hear a decent new 6SN7 or 6SL7 for that matter.

Under $1000, even under $1500 is cheap for an amp. Spend the money for the Prima Luna or the Cayin and when you have some extra dough, replace the tubes. A good deal will come along. Have a few sets for different kinds of music or to compliment different speakers or just to suit your mood.

The theory that the better amp will reveal the better tubes is a good one but you'll yield about 90+% (maybe 95%)of what the tube compliment is capable of with either of the afore mentioned amps.

As far as the car metaphor goes, replacing the tubes is more like replacing the engine than replacing the tires. The theory that different amps will not realize the same benefit of different tubes because of the way the circuitry utilizes the tube is also true but not to any great degree. Most all audio circuits have very similar objectives and parameters.

Hope this helps someone.