I'd even guess they Hegemony only upgraded their Onslaughts with shields and hyperspace travel drives after the arrival.

About three months after the Collapse, a Domain task force emerged from hyperspace in the sector.

from the state of affairs, so that's definitely not the case

What sort of distance would be covered by a gate connection?

let's see (data crunching below):

the following data is obtained with 1 point in navigation

the Onslaught (slowest ship in taskforce pollux) goes 7 burn in hyperspace at 30 fuel/day, at 25 fuel/ly, meaning she travels at 30/25 = 1.2 ly/day

the Atlas (also possibly the slowest ship in taskforce pollux) goes 7 burn in hyperspace at 12 fuel/day, at 10 fuel/ly, meaning she travels at 12/10 = 1.2 ly/day

some other data below, showing a slightly less efficient burn efficiency, but it's possible that max burn is not a linear function, but does drop in efficiency as it reaches higher ratings

Spoiler

the Tempest goes 14 burn in hyperspace at 1.5fuel/day, at 0.8 fuel/ly, meaning she travels at 1.5/0.8 = 1.875 ly/day (divide by 14 and we get 0.13 ly per burn per day)

the Shuttle goes 12 burn in hyperspace at 0.4fuel/day, at 0.25 fuel/ly, meaning she travels at 0.4/0.25 = 1.6 ly/day (divide that by 12 and we get 0.13 per burn per day)

the Ox goes 12 burn in hyperspace at 8.5fuel/day, at 5 fuel/ly, meaning she travels at 8.5/5 = 1.7 ly/day (divide that by 12 and we get 0.14 ly per burn per day)

the Enforcer goes 9 burn in hyperspace at 4.2fuel/day, at 3 fuel/ly, meaning she travels at 4.2/3 = 1.4 ly/day (divide that by 9 and we get 0.15 ly per burn per day)

the Hammerhead goes 9 burn in hyperspace at 2.8fuel/day, at 2 fuel/ly, meaning she travels at 2.8/2 = 1.4 ly/day (divide that by 9 and we get 0.15 ly per burn per day)

at this point I figured we have enough data and stopped collecting. Rounding errors and such aside, we can see that 7 burn means 1.2 ly/day

now, as far as we know, by year 2013 task force pollux has not left on its task (from Earth or elsewhere), which means it has at most 3126-206-2013 = 907 years at 1.2 ly/day to reach this sector (the reality is probably a lot less, but this is say if the fleet leaves tomorrow). The max possible distance covered by pollux would be 907*365.25*1.2 = 397538 ly.

Considering milky way goes about 120,000 ly across, that doesn't really say much. However, considering the nearest galaxy (andromeda) is way far away from that at 2538000 ly, at least we established that we're still in this galaxy