Just that, a solid nope. Normally I'd ask for some more information, but not only you said to just assume they can fly, you said it yourself that groundbirds are only capable of flying for relatively short distances and have a lifestyle that relies very little on flight. Much like ducklings raised by chickens alongside chicks don't suddenly become afraid of water, your groundbirds won't become magically capable of doing everything a hawkling can just because they were raised by one. Wings present in soaring predators like eagles and hawks are usually long, large, powerful and adapted to enable them to use wind currents to keep themselves in the air with minimal energy. A creature with small, broad wings, no matter how much encouragement it gets, can't get the same results without the same wings. It's like wanting a kori bustard, heaviest flying bird in the world, to take off with the same ease of a harpy eagle and make tight turns like a bat. It ain't happening unless we add in things like magic or anomalies that break the normal laws of the universe as we know it.
If you're having trouble with their anatomy, I recommend taking a look at larger raptors and juvenile T-Rexes, as they had longer tails, a ground-centered lifestyle and were adapted to function as nimble predators. Birds that rely very little on flight, such as roadrunners, might also be worth a look.
Edit: while your groundbirds might have human-level intelligence, that doesn't change much here. Humans have used their intellect and the knowledge we've accumulated over the years to build things that go beyond what common biology is capable of. The largest plane far outweights and oitsizes the largest flying animals to ever live. However, one thing remains the same: our technology has only gone so far in increasing our own limits. We might be able to live longer and know more efficient ways to train our body for certain purposes, but despite all of our knowledge and intellect, we'll still get absolutely bodied in a fight against an angry chimpanzee, and a human raised by a chimpanzee could never hope to get close to it in terms of climbing ability, sheer strength or speed.
In other words, unless they have some crazy advanced science in the fields of bioengineering, your groundbirds' intellect can only do so much to expand their natural capabilities. Meaning that, even when accounting for their intelligence, they'll still only be able to fly for relatively short distances, with little to no hope of soaring high.
What you could see is a groundbird raising a hawkling and teaching it how to move around on the ground and how to hunt properly. They won't be as good as a groundbird due to the fact that such teachings are specific to the groundbird based on their own anatomy, but the hawkling will have the knowledge, being able to try out ways to make use of it based on their own physical abilities and limits, because in here we're not talking about a physical ability that's clearly exclusive to the members of a certain species, but rather about knowledge that can be made useful by any species with enough intelligence to process it.
Basically, can intelligence alone without the use of genetic modification allow your groundbird to overcome natural barriers and soar through the skies along with their hawkling parent? No, just like no human today can even hope to swim with the same skill, speed or agility of a sea-lion or seal even with the best diving skills in the world and while using the greatest scuba gear in the market. Can they potentially learn something useful from what the hawklings know and adapt said knowledge so they can use it based on their own physical limitations? Pretty likely.