I use Herbie's tube dampers and, for me, I can hear a difference. Mostly on the AX7's. I've also used Herbie's on the tubes in my BAT CD player and I can hear a difference there.
The difference is subtle (unless the tube is obviously micro-phonic). First, you lose some of the "air" or ambiance - not necessarily a good thing. The bass seems to increase a little or tighten up (a good thing). Finally, a little bit of distortion seems to go away (a good thing). All tubes are a little micro-phonic. With tube dampers across all the signal tubes, some of the tube "magic" will disappear and the sound will get more solid and can seem sterile. So, you may want to try damping some but not all of the tubes.
Your ears, system, etc. may be different but these are my findings.