If the noise spikes were of sufficient amplitude and wideband then it'd have an adverse effect on the diff amp stages as you say. Perhaps the Zyxel has a shunt for that situation built in.
However such spikes are more than likely local to the modem (eg conducted & radiated mains noise) and best dealt with at source if possible.
I wouldn't imagine Weaver has too much of that from neighbours so most of the noise on his line is likely to be locally generated - the remotely induced noise will suffer the same attenuation as his DSL signal anyway so not a lot can be done there in terms of improving things.
My usual starting point for this sort of stuff is to use a cheap UPS to run the modem (Sky router here has some ancient Belkin cheapo UPS feeding it) and a laptop then flick the mains switch at your fusebox.
Run your stats programs and look for a difference on the graphs. If there is then go play detective & find what's generating the noise - here it was some second-hand PS/3 with a very noisy power supply which I filtered with one of these :
http://www.maplin.co.uk/p/tacima-2m-six-socket-mains-conditioner-plus-rfi-filter-for-home-cinema-and-hifi-l07bk (didn't pay that price though, they're on Amazon). Someone else on here used the same filter to sort out a noisy treadmill. Its got a very decent filter but is stupidly expensive for what it is.
In the case of locally generated mains noise its better to filter at source - ie don't connect the mains filter to the modem/router, connect it to the offending mains-powered items.
Not trying to teach anyone how to suck eggs but eliminating conducted/radiated interference isn't always as obvious as it seems, so its best to start from the point of "is there a problem in the first place?".
I'm also assuming that Weaver has a UPS - damn sure I would if I was living up there in Winter