Yes, they can. And they must process more than 1MB of data in order to validate what they are calling a 1MB block. The difference in quantity of data, of course, being the amount of data in the signatures.
That was what I initially said. This depends on the exact quantity of data though, just how much more are we talking about here?
So tell me again why this does requirement for more data not lead to node centralization, when many SegWit boosters (perhaps not yourself - I can't keep track) rely upon 'increasing block size to 2MB will lead to node centralization' as one of their strongest arguments? Or at least as their only argument for their claim that a simple block size increase is unsafe?
I don't rely on that argument but I have surely used it a number of times (can't recall all the discussions). I'm just not aware of an estimated factor of increase and have chosen to ignore this information until I have one. Has someone done the math?