Sure you can do that. Of course l the trick will be to find a tube amp that will get along nicely with your your current pre, but that would apply to any Pre-Power Amp combo regardless of what technologies either of them employ.
I spent many years running a tubed pre (ARC SP-( with solid state and hybrid amps (Moscode 600 & Classe Twenty Five.) I think tat this is the easiest and most economical way to inject some "tube sound" into your system, especially if you have speakers that require high wattage.
I eventually got a tube amp (ARC VT-200, which sounds amazing, but it needs 26 tubes to put out the 200 watts I needed which can get very pricey to run over the long term.) On the other hand the SP-9 has only 2 6dj8s which sets me back about $50 for a full retube.
And in addition to just replacing tubes as the wear out, repairs to a tube power amp can get pricey as well since because of the higher B+ voltages required to operate power output tubes, when a tube amp does fail, it very often does so in a big way.
That said, in spite of the headaches and costs involved with them IMO, there is nothing like a good tube amp. Recent solid state designs are getting closer than they used to be, but I am still a fan of that tube magic. (YMMV)
That said, I still think getting a good synergistic match among the Pre amp, Power amp and the speakers is still more important than what technologies you end up using