The origin of your ticket will probably be Manchester Stns, but your reservation and itinerary will start at the actual station you pick, and it's that that matters. Near enough all Northern trains are "reservable" so you will get a reservation on your itinerary.
As I said it's very likely you would get away with it because it's clearly not trying to get away with a lower fare, but it's not 100% certain that you would, you'd just have to meet an awkward RPI and your ticket would be worthless.
Some would argue that if you buy an Advance from Manchester Stns you can take a connecting service from any Manchester station to the one booked as long as the ticket's route is respected (it's probably +Connections which means any TOC). However, this is for some debate and not all staff will consider that reasonable, and it only takes one awkward one to miss your train and lose your ticket value. Thus the only sensible advice with Advances is to do exactly what your itinerary says.
A single from Picc to Deansgate is £2.80, or about £1.90 with Railcard, by the way. On the basis that even an Advance for that trip isn't going to be particularly cheap, it's quite a risk to take to avoid paying that. Assuming just going from Oxford Road either way doesn't work, I'd book it from Deansgate and buy that single if I did want to go from Picc. Or take the risk, but the walk up single (there's only one, Anytime Day Single) is £68...
