Hoping to create a heartiest stew, I was thinking of roasting my carrots, okra, and sweet potatoes. Will it create any substantial change in flavor?
You will get the roasty, caramelized flavors; how much influence they will have on the overall flavor of your stew will depend on several factors including:
Roasting the vegetables will also cook them, so you will want to add them to the stew much later, so they don't overcook.
If you google roasted vegetable stew, you will find several recipes for inspiration.
As to whether this is a superior, or heartier flavor, that would be a matter of opinion. You don't mention roasting celery or onions (partners with carrots in the classic mire poix), but these are also excellent candidates for roasting, as are all types of root vegetable.
Roasting your veggies will give a "richer" and somewhat sweeter flavor to your stew. As mentioned in another answer, your cooking times are reduced by pre-roasting. Also, it's been my experience that pre-roasting or deeply browning your meat will Vastly improve your stews!