I've done the pedal to the metal with a cold ICE in my wife's Clarity and yes, the ICE revs really high, but it provided zero to the car's acceleration.
I doubt it's zero, unless you are speaking figuratively. If while driving EV I go just past the blue into the gray area, causing ICE to come on, you barely hear the engine and that may be closer to zero, but when you floor it the revs go much higher so it is contributing something, although maybe not as much as if the engine is already somewhat warmed up. Although having a warmed up engine in EV mode is somewhat rare, unless you happened to have just switched from HV to EV a few minutes before the hard acceleration event occurred. When you are driving in EV mode a hard acceleration is generally a one time event caused by some circumstance (short onramp, avoiding a hazard, etc) and it will likely not be repeated for the rest of the drive time that you are in EV mode, so the now warmed up engine is unlikely to be called upon during that particular drive. That's why I am skeptical of the common belief that while driving in EV mode you have this great surge of power just waiting to be called on by pressing the pedal past the detent. But since in almost cases the engine will be cold, I think it's unlikely to contribute all that much power. But since the Clarity lacks the Volt's power gauges, the only way to really know how much additional power that you get from a cold engine is to hook up a dymo, or do several 0-60 tests both warm and cold. But they need to be controlled repeated tests, i.e. exact same section of road, driving conditions, etc. and do multiple identical 0-60 runs then average them together as well as throw out any outliers. It's something I have been meaning to do, but whereas it's easy to do multiple warm engine 0-60 runs, cold engine is much harder because you can only do one, then the engine warms up and that's it for that day, you have to wait another day to do another cold engine test.
As for how rare, consider what you have to do when getting on a short uphill freeway on ramp where traffic is moving at 55-70 MPH. You really need to be moving with the flow of traffic when you reach the start of the merge area to give yourself room to adjust. This is a weakness in the Clarity that it requires both the electric and gas motors to get full power.
For most people I think that is rare. Most people don't have freeway onramps that require literally putting the pedal to the floor in order to be at traffic speed when you merge. Someone who has on onramp like that which they use every morning when going to work, sure for that person it is not rare. But for most people I think having to press the pedal to the floor is rare, not a daily or even weekly occurrence.
Well there is a type of person who it is not rare for, the type of person who shoots out in split-second gaps in traffic in front of other cars and then has to put the pedal to the floor to avoid impeding the car that they just pulled in front of. But that is not safe driving, so I don't consider that as a normal situation that most people encounter on a regular basis. I really think that for the vast majority of people and the roads that they drive on, pedal to the floor is usually only needed when the driver has made an error in judgment and they need massive acceleration to get out of the situation. I can think of very few cases where putting yourself in a situation that requires having to press the pedal to the floor would be considered part of safe driving. To me it's like ABS, it's there if you need it but if you are using ABS every day then something about your driving habits is wrong. Again someone may live somewhere with specific unique driving situations that absolutely require pedal to the floor on a regular basis, but that would be an exception, and even then I question whether it's really required or they just are too impatient to wait for a safe gap, or they don't want to turn right instead as that will take longer, so it becomes an excuse "I have to jump out there or I will be there all day". Sort of like people who claim you have to drive over the speed limit on the freeway "or you will get run over". That's just an excuse. It is quite easy to safely drive the speed limit even when other traffic is going faster, you just stay as far to the right as possible and maintain a steady speed. People get on your bumper even then, but that's not because they couldn't slow down in time it's because they want to intimidate you into speeding up because their offramp is coming up and you are in their way. I normally use cruise control on the freeway and I just let them sit and fume and they usually either back off or go around me.