At what Mach Number do variable cycle engines (VCEs) start showing benefits over turbofans?
It's not a high Mach number that gives a variable cycle engine an advantage over a turbofan. Most air-to-air combat happens at subsonic speeds, because drag gets very high when you start trying to turn sharply at supersonic speeds. For combat, you need high specific excess power (SEP), which comes from a low bypass ratio turbojet. But, cruise speeds are also typically 0.8 to 0.9 Mach, even for fighter jets. But lower fuel consumption in cruise occurs with a high bypass ratio turbofan. That's because the exit velocity is not much higher than the aircraft velocity, which means the propulsive efficiency is high. But, it means the aircraft doesn't have excess power, to suddenly accelerate, or stop energy bleeding off in multiple, rapid turns.

So, in both cases, cruise or combat, speeds are subsonic, but the desirable type of engine is quite different. To illustrate, the specific fuel consumption (SFC) of a CFM56-7 is about 0.37 lb/hr/lb, with a BPR of about 5.4. In comparison, the F100-PW-229 has an SFC of about 0.73 lb/hr/lb (non AB), and a BPR of about 0.36. That's pretty close to a factor of two. Obviously, a VCE engine can't change the bypass ratio as much as in this example. I don't expect the variation of bypass ratio (BPR) in a variable cycle engine is published anywhere.

So, the advantage of a VCE occurs even if you don't need or want to fly supersonic. The advantage occurs when you suddenly need excess power, even at subsonic speeds. Military aircraft benefit from a variable cycle (variable BPR) not because of the large speed range over which they fly, but because of the wide variety of mission types they fly. Civil aircraft just need to be optimised for cruise. Variable cycle allows military aircraft to be better optimised for combat and cruise, not just the first.