Preamp is an amplifier too, right???

When I was studying electronics I was never introduced to such component as preamp. The whole section in electronics were dedicated to amplifiers and they are only realy different with output power.
If preamplifier is basically an amplifier than it certainly have an output power only you can't use it to drive speakers since the output impedance might require matching
I'm not familiar with 2a3 monos but pretty familiar with the bulbs' output characteristics. It realy seems to me that by cranking volume on your SS-pre you're getting these tubes onto clipping. Since they're working far away from their specified region, they might end life pretty quick.

Preamps depending on their circuit topology (and there are few ways to design an input driver) can produce an output power(especially ss-preamps).
There are also SS-preamps(base- or gate- coupled output stages) that do increase voltage in very-small sacrifice to current thus still able to increase power as well.
I did an experiment just like Sean mentioned by simply connecting an output transformer to Bryston B11 preamp and than to small monitor speakers(only to play with) and it worked but clipped not even reaching 12 o'clock...
An output power tube basically has a very large output impedance thus also mainly amplifies voltage. It certainly requires either transformer or reverse-polarity load(negative feedback) as it's done with OTL.