Greetings from the 60th parallel, where we ride studded tyres 5 months out of 12.
What is the likelihood of the spikes puncturing the tubes?
The first factor which this likelihood depends on is the tyre mark. My commuting friends have been telling stories about Schwalbe (Marathon or not) Winters doing that; I did not believe them until I got this:
(Naturally, this was not the only one place where the spike has rubbed the tyre through - this was the first one which punctured the tube.)
I never heard similar complains about other tyre marks. If you compare the thickness of the rubber in places where the studs sit in Schwalbe Winter and for example Nokian W106, you see notable difference. Schwalbes are lighter, and this is the price.
Will this load cause the spikes to puncture the tubes?
My feeling is that it's the amount of rubbing which mostly contributes to such, well, rubbing through. This amount depends on how much the tyre deflects, which in turn is a function of the applied weight and tyre pressure. So (assuming my feeling is correct) you can reduce the probability of such internal puncture by running higher pressures.
My solution to the problem was: not save weight here and buy more sturdy studded tyres; use some liner with the Schwalbe Winters (not yet rubbed through) I have. A cut-along tube or a special anti-puncture tape might carry you through the winter (or they might not).