Well, every "body" (literally) is different, so I imagine it might take some people a couple of weeks to adjust. But, I've spent a lot of time in Mexico City and Quito. Therefore, did some research. Here's what I learned.
8,000 feet is a cut off in the minds of most who study this. Acclimatizing above 8,000 feet is very difficult, for reasons that I used to understand.
Mexico City is at ~7,300 feet; Quito ~9,300 (Denver, for comparison, ~5,300 feet...not called "mile high" for nothin').
Most healthy adults (people with heart or lung conditions, kids and the elderly are different) can adjust to Mexico City in a couple of days and feel "normal" after three days.
World Class Athletes, with a full week to adjust, are probably going to experience minimal effects by day six or seven, but it will differ player by player.
I'm nobody's definition of a World Class Athlete, but I try to keep in good shape for my age and was usually able to do my normal work out in the hotel gym after three days days (air filtered for pollutants!!!) in Mexico City. World Class Athletes should be able to perform at close to expected levels in a week. Anyone who doesn't should see a cardiologist when they return, as there might be a problem with how they absorb oxygen into their blood. No fooling. They should see a doctor who is looking specifically for cardiac issues. Amazing how many "healthy" people drop dead of heart attacks every day because they didn't get the right kind of care.
Most important: no alcohol; drink a lot of (bottled) water; get extra sleep, since your sleep is interrupted the first few nights...not sure why, but I'd keep waking up. Did I mention, "no alcohol?" By night three and day four, I was always fine.
Quito is another story entirely. The extra 2,000 feet really made a difference to the degree that oxygen canisters were available at the end of the ramp leaving the plane. I never felt "normal" until I was there well over a week and never ventured into the gym until then.
Air Pollution will be a much greater issue for the Pats, who have been working out at 7,200 feet for the last week.
So, yes, I think they will have a real advantage over a bunch of idiots who just fly in the night before...dumb and dumber. They will be literally gasping for breath after the first quarter.