No, the power of a tube amp will not increase as speaker impedance decreases. A tube amp will provide maximum rated power only when the speaker load is matched with the output impedance of the tube. Any mismatch will cause a DECREASE of power - regardless of which way the speaker load changes.
The way to match a speaker load is with the output transformer. Using a 2A3 tube, eg, the power rating is 15 watts with a plate resistance of 2,500 ohms, which is also the output impedance. If the load to be driven is 8-ohms, then the output transformer has to reflect 2,500 ohms at the primary when the secondary is 8-ohms. The reason for the 2,500 ohms at the primary is to match it to the tube's output impedance. When these impedances are matched, there is a maximum transfer of power from tube to transformer. All 15 watts are transferred, which is then passed along to the speaker.
If the speaker load changes to 4-ohms and 16-oms, then the primary impedance will change to (reflect) 1,250-ohms and 5,000 ohms respectively, which by ohms law will transfer 13.5 watts to the xfmr (in both cases).
Multiple tap output transformers are used to match different nominal speaker impedances (or else an amp manufacturer will have to wind different transformers and if you change speakers you'll need another amp). It doesn't matter what impedance the speaker is - as long as the appropriate tap is selected, the amp power output will remain the same. If the taps are not properly selected, the amp will put out less power.
A solid state amp can double its power as speaker impedance is halved if and only if the power supply transformer can provide the power necessary for the increased current. Why can't a tube amp do this? Because the power is lost from the tube output to the primary OT transformer winding when the speaker impedance changes. Loss of power equals loss of current at constant voltage, thus the power decrease.
