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?
In Wuillie's presentation at Scaling Bitcoin Hong Kong, I believe* he stated that by looking at recent transactions, the current scaling factor would seem to be about 1.75x. Or that signature data is slightly less than half the block data.
*my memory is at times faulty. But I'll stick to a claim that some prominent Core dev stated that analysis of recent blocks led to this figure.
Others I have seen use a 4x figure - totally dependent upon an assumption that multisig become a much larger portion of the transaction volume.
For this little branch of the discussion, the salient point is that any node that performs validation (i.e. any node operating in a trustless manner) must process not the claimed 1MB block size worth of data, but an amount of data that reflects the signature data as well - 1MB multiplied by this (instantaneous) scaling factor, be it 1.75x, 4x, or whatever else represents the proportion of signature data associated with the transactions included in that block.