There may well be limited carry over into adults, and there is a lack of research in the area of QM for adults (understandably) however, it stand to reason that being able to work and move effectively using 4 limbs, consciously rather than 2 (just legs) may engage your body and mind in a more challenging way compared to using less of your body at any given time.
From experience, quad movement brings on the sweat, makes the lungs and heart work hard and forces you to be more conscious in your movement, especially when moving slower, deliberately place each foot, hand and body part to move yourself. Coupling this with balancing on or in smaller spaces adds an extra element of difficulty which is a recommended progression for improving movement ability.
One such exercise I've been developing and training is making an assortment of rail/bars/beams and forcing yourself to keep moving in the, without touching the groun, using your arms as much as you would your legs, try even a minute of movement in this manner and you'll see what I mean. In spending more time in this type of movement progressively, you're develop wrist, forearm, bicep/triceps, shoulder and surrounding musculature strength/ability simply by spending more time in more movement patterns, supporting and controlling your movements with upper body limbs.
The more experience in movement, in different rotations, directions and stances, the better your ability to apply yourself to a new or similar situation as and when they occur.
In the grand scheme of movement, we're more likely to need to move on our feet and use our hands/arms secondarily but as for training and learning, give it a go.
Crawl more, move more and have fun!