During exercise, there is a process called “contraction mediated pathway of glucose uptake”. This pathway allows glucose uptake to happen without much insulin.
Adenylate kinase converts adenosine diphosphate molecules into adenosine triphosphate (ATP) and adenosine monophosphate (AMP). The ATP is hydrolyzed for energy. The AMP attracts 5’-adenosine monophosphate-activated protein kinase (AMPK).
AMPK ultimately does the same result as insulin - causes GLUT4 to go to the cell surface and allow glucose uptake.
But all of that aside, it isn’t exactly the same as insulin. You can’t just eat a slice of pie and start walking. It has to be of sufficient intensity and duration for this to happen.
Depending on individual factors for each of us, it may happen at almost the same intensity where your body would be releasing cortisol from the exercise stress, which means your body might be releasing liver glycogen at the same time! So right when your body starts to be able to take in glucose without insulin, your liver might be spitting out a bunch of glycogen. Oh, crap! Thanks for nothing, liver!
So the answer is “yes” it can happen, but it takes a lot of work to get to that point. And you may not even realize it, depending on when your body starts signalling stress.
The best way to find it would be to hit a long and hard run, just below threshold pace. And you would need to get to that point and have no residual insulin in your body. It’s tough to get there!