So having fairly sensitive speakers has you peering into the rabbit warren of tube gear. That's understandable, but be warned that the whole tube realm is rife with marketing nonsense and enthusiastic adherents who have little clue how any of this all actually works on a reductive level.
Yes, you can get a tube amp and feed it from your AVR's pre-outs.
No, that would not defeat the purpose, if the purpose is to hear what a tube amp driving your speakers sounds like. The proverbial "tube sound" results from tube amplification driving transducers, not from tube buffer stages, whose loads are much easier than a speaker.
Yes, it would likely defeat the purpose if clean, linear response is the goal, but some folks find the audible changes that tube amps produce pleasant.
No, the AVR would not be the weak link in your proposed setup. The tube amp would be the limiting factor.
As far as audible differences, tube gear can span from virtually indistinguishable from ss to highly colored. More specifically, a well engineered, high power pp tube amp would be difficult to pick out by ear, and would necessarily be a complex, very costly affair. Flea watt SET amps, the most rudimentary and simple amps, provide the most colored, tubey sound. SETs are the darlings of many of the old Klipsch farts, fwiw. Despite their simplicity, they too can be very pricey.