Yes they would, but by the time they get there would they want to?
Changes like this usually start with a lot of death, this is no different. Let's assume Loki has been friendly enough to make sure the crowmen can completely control their body and to open any doors, windows and entrances we need just to get in and out of our homes, work and facilities. From a quick search Crows seem capable of surviving in a range of hot and cold climates, so let's assume most crowmen survive their chosen environment despite suddenly not being able to wear their normal protective clothing. Now we still need to watch out for all the birds of prey that might want to eat us (and all the cats, dogs and other pets that don't have a problem killing/eating crow), and we are now surrounded by machinery, homes and tools all build for humans. Food is going to be hard to get by and many many crowmen will starve.
Humans are resourceful, so the crowmen will organize and try to start rebuilding society. This means repurposing what tools they can, and starting to recreate societies: Reinvent homes for crowmen, creation and gathering of food, construction of tools and generation and transportation of consumer goods. They will likely commit genocide on several forms of bird of prey until these birds stop eating the crowmen, but humans aren't very concerned about mass-extinction on the best of days and if it's a creature that's actively killing them any qualms about murdering every last one go out the window.
Since most infrastructure of the human empire is useless (although the cabling and pipes already laid down will be useful) the crowmen will need to rebuild just about everything. Here they hit another one of their big hurdles: Hand-eye coordination. Crows have less of it, as they either use their beak which makes seeing what they are manipulating a bit harder or they use their claws and can only really use one eye at a time to see what they are doing.
Another big hurdle is transportation. Humans load in stuff by hand all the time, on trains, trucks, boats, lorries, planes, from a conveyor belt into a box... All that is a lot harder for a crowman, especially for larger parts that need manufacturing. This means a far larger reliance on tools and machinery to do the carrying and moving for the crowmen.
As you can imagine it's going to take several generations before crowmen are back to a space-age civilization. They'll get there eventually. But when they have that technology... Do the crowmen of that time want to be human? Humans can't fly, they'll have technology all build for small crowmen and not for large humans. The generations that get the choice have all been raised by crowmen and have only ever known to be crowmen. I think it's more likely that they destroy any chance of turning back to humans. Having human intelligence in such a small body that can fly is probably incredibly useful in the long run, if only for how much food you need for the world population.