Can an all-tube guitar amp be damaged by flyback voltages?
The keypoint here is the "reflected impedance" due to the use of an output transformer.

Let's assume we have a 6L6-based Class-AB p/p stage and we want to drive a 4R load. The nominal output impedance of this stage will be around 4k. So the output transformer should have a turns ratio of sqrt(4k:4R)=~33. 

A speaker can be thought of a "motor". A higher impedance load will develop higher flyback voltages due to Ldi/dt. So, if you connect a 16R load to 4R output then the primary will see around 16k which means higher spikes (flyback voltages). This is dangerous if you play at "high volume".

Although today's output transformers are strong enough, it's strongly recommended not to exceed 100% of mismatch. Of course the best performance will be achieved on a matched output.