The growth of a turbine due to heat is a well-established science. The only question is whether the cold-running clearance is so far away from the housing that a difference in turbine inlet temperature between a cooled exhaust and an uncooled exhaust makes a measurable difference.
So the first question is, how much hotter is the exhaust without the extra water jackets? My guess is probably not more than a couple hundred degrees.
If that's right, how much will the turbine and housing grow in moving from, say, 1000°F to 1200°F? If the cold running clearance is tight enough, it could be a significant closure at higher temperatures.
However, you have to figure that Cummins wants to avoid the turbine rubbing the housing at all costs. That suggests large clearances, even at maximum inlet temperature.
We don't have enough information to dismiss the idea that it is turbine growth relative to the housing that improves the turbine performance. But as others have mentioned, the waste gate will ensure that any extra power available to the turbine will be dumped overboard once the waste gate opens.
Of course, higher heat means more turbine power. Gonzo put it nicely when he said the turbo is a heat engine (of course, so is the reciprocating engine). The first law of thermodynamics tells us that heat=power. It's that simple. So one could argue that higher turbine inlet temperature would build boost faster, since more power is available.
To answer the original question, higher EGT could mean more boost, except that the waste gate prevents this. Higher EGT probably will yield faster spoolup, so in that sense it's "more boost per unit time" until the WG opens.
-Ryan