Yes, I would guess the plant has little or no active working root system. The best way to find out is to take it out of the soil and look at it. This is precisely the worst time of year to be doing that though, given your northerly location and the low light of the season. So, you know, wait a few months or check it out now, as you like. The key is to avoid watering right after you put it back in the pot. Give it a week (or two, if there was root damage in the process of handling) sitting in dry soil before you water for the first time. The risk of rot is especially high given your location and the time of year.
The presence or absence of roots may help explain the current malaise. Water stressed aloes (including plants that are rootless or nearly so) will tend to burn through their lower leaves (dying back from the tips) in order to salvage some water from them. To some extent this is normal, but obviously when the rosette is shrinking like yours is, there must be some chronic water deprivation going on (or its functional equivalent, root loss).
In any case, the soil looks good, and the pot may be a good size (depending on what you see when you unpot the plant). When I water aloes (dozens of them on the patio here) I completely saturate the soil, allowing all the excess to drain out and away from the bottom of the pots. Then wait however long it takes for the soil to go mostly or completely dry at depth (not just the surface) before watering again. Experience tells me how long that takes. Essentially it's an ongoing cycle from wet to dry and back. That cycle will take longer during late fall and winter (a month maybe for your plant, in a bright space) and it will take less time during the warmer and brighter months of late spring and summer. Where light is very limited, as may be the the case in your location at this time of year, you may want to water short of saturation, to be on the safe side.
There is no particular benefit to leaving the soil bone dry for any extended period, but there is an increased risk of rot if the soil stays too wet too often. A fair amount of rock in the soil (which I see in the photo) helps make the drainage issue easier.