The tube NEVER has the same function as a transformorer in a microphone. And yes, if the tube is doing it's job in the mic, it is amplifying the signal (but not up to line level obviously).
Yes, the tube is amplifying, but mainly in the strict sense: adding amps (or mA, more likely).
The basic job of the tube is to provide a buffer for the extremely high-impedance condenser mic capsule. Another way of putting that is impedance conversion, or simply current gain.
While a tube can (and often does, but see below) add voltage gain, that is not the main function of a tube in a microphone. After all, large diaphragm condenser capsules are very sensitive and put out plenty of voltage--just very very little current.
So it's not exactly proper to say that a tube mic "amplifies the signal, but not up to line level", since the main job of the mic's amplifier circuit (whether FET or tube) is not to provide voltage gain.
The job of transformers in microphones is very different according to the type of microphone. In a dynamic mic, it will be a step-up transformer. That's because a dynamic capsule is low-impedance (like a speaker) and low-level. The transformer adds volts at the cost of amps. So you have a mic-impedance output at a higher level than the signal straight off the capsule.
In a condenser mic, it's usually the opposite: a step-down transformer. These are very common in tube mics, because despite what I said above, tubes used in mics are better at voltage gain (although there is also significant current gain, and we could argue about plate vs. cathode design, etc.), so the tube will increase the level somewhat, which is given back in the output transformer. This is necessary because the tube output impedance is still kinda highish (tens of Kohms, still better than many, many megs!), so the transformer converts that extra voltage into extra current, for the required low output impedance.
Of course, the tube could simply be followed by a solid-state stage, which wouldn't lose the voltage like the transformer does, but: a) that would be a really hot output signal, and b) transformers are cool