Do Alzheimer's patients have spaces in their brain with low interstitial space?
It's hard to judge whether interstitial space changes are due to beta amyloid accumulation or because the Alzheimer's brain has suffered such profound cell loss and neurodegeneration as a result.

The Nedergaard paper you quote is more about a daily cycle of increase/decrease in interstitial space related to the sleep/wake cycle [Ref 1]. Specifically, that during sleep, there is more space to flush out the brain including beta-amyloid.  One interesting hypothesis from that being that perhaps the accumulation of these aggregates is actually due to inefficient sleep -> inefficient flushing of plaques which go on to give symptoms.  So even if the interstitial space in what's left of the Alzheimer's brain remained the same as a healthy brain, the problem of beta amyloid clearance could still be present.  It remains to be seen if one could restore normal clearance whether degeneration could be slowed and symptoms abated.

[Ref. 1]: Paper from Nedergaard group