The water hole tunnel is one of my favorites but it can be pretty mungy and care is needed not to silt it out. Even a slightly errant or overly aggresssive frog kick can stir up the mung. A flutter kick would clearly be problematic.
Personally, I feel strongly that people with crappy skills like that need to stay in the more or less "sacrificial" training areas of the cave until they get their stuff together, if they ever do.
A couple things to consider would be the ease at which you can silt out a tunnel like that, and in particular what may happen afterwards. The line in the water hole tunnel is old, slack and would not be ideal to have to come out on in touch contact. There is also a sidemount tunnel that branches to the right about half way back from the waterhole. That one gets tighter and if you got on it in by mistake in a silt out, it could get interesting with part of the team in backmount.
The waterhole tunnel in general is also large enough to easily turn a team in most places, so if it were me and the lead was going to fast and/or flutter kicking and creating silt problems, I would get his attention and both slow him down and make him aware of the silt issue he was creating. If he repeated, I'd get his attention and thumb the dive, both for the sake of the team and out of respect for the cave and the concept of cave conservation. The idiot leading had no business being there.
In terms of speed, once I get above my optimum cruise speed CO2 retention goes up as does my SAC with little real gain in penetration distance. There are situations where swimming faster helps. It is much like flying into a headwind, a little more speed, within limits is worth the fuel burn in terms of extendced range because it reduces the time in the head wind. Similarly, if you are swimming into flow at a leisurely pace and are barely making headway, you won't get much penetration, so there is a time and place for a faster pace. The waterhole tunnel is not one of those places and it is rare that the flow in the peanut tunnel would be high enough to justify a faster than normal pace.
Of course, you will encounter divers who swim fast and skip breathe in order to maximize penetration. Those are also people who end up being more susceptible to narcosis due to the exacerbation by the elevated CO2 levels, in addition to the effects of the CO2 itself, and they often end up with CO2 headaches during and after the dive. If you need more distance in a cave, bring a stage or larger tanks.