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It is possible, everything will work fine. When you sort items by any field paged items will be sorted as well. You just need to use something like Paged=TRUE&p_SortBehavior=Modified&p_ID=7 in ListItemCollectionPosition.
We contacted MS Support regarding this issue. They said that one of Windows updates breaks form digest generation. They confirmed that it should be fixed in the next CU - June 2013 or whatever comes next.
No, this is completely out of the box site collection based on Publishing Portal template. The thing is that request digest is validated, but it contains "InvalidFormDigest" string which is obviously not valid.
