It is not so much a problem with the boiler running dry as it is with the amount of steam power available. There is some steam stored above the level of the water, but the "super-heated" water is actually over the boiling point because it is under pressure. As steam is released, the stored heat energy in the water is released in the form of steam. Eventually the heating element cannot keep up and the power of the steam decreases. There will still be a bit of steam, but the force of the stream will be only marginal for stretching milk.
I suppose, beyond that, the question is, how much do you need? There is sufficient steam to stretch milk for three, or maybe four cappuccino. if you need t stretch more than that the problem becomes how long it would take to make that many espresso shots and how long they would sit before the milk is ready.
OK- the answer is that I dont know because I dont remember anyone actually testing it... For the reasons mentioned above I would have to guess.
So that you would not have to deal with it or worry about it, the solution is to stretch the first 8 to 10 ounces of milk, then refill the boiler using the hot water function, and allow the boiler to come back up to temperature before steaming again.
If you need continuous steam power for extended periods of time, pick up a second-hand machine with a thermoblock steam function or get a dedicated steamer,,,? Just spitballing..