If you're willing to feed live food for the life of the seahorses, and you have backup plans for when lfs's are out of food, it is possible. I've kept wild caught reidi before, and the biggest problem was convincing them to eat frozen. I don't think any did reliably. I could get them to eat frozen ghost shrimp if I waved it in front of their faces with tongs, and occasionally mysis (the girls seemed more inclined to try new things).
However, feeding live to seahorse can be extremely expensive. I think there were months I spent over $100 on food and when one fish store in the area was out of ghost shrimp, it seemed like they all were. Plus, ghost shrimp isn't the best food since its from freshwater. Setting up a mysis culture is time and space intensive and difficult to maintain.
This was all before CB seahorses were readily available. CB seahorses are SUCH blessings. My life was just about getting my seahorses fed back then. Several trips to the LFS each week, ordering food online, etc . . . Eating cheap food so I could afford food for my seahorses.
If you're anywhere near the ocean, you might be able to collect your own food.
Oh, and they won't last long eating only brine shrimp, so rule that out right now.
In terms of diseases, I've always found wild caught reidi to be pretty hardy. They should be dewormed but they aren't particularly sensitive to diseases, unlike some wild caughts. But never mix with captive bred seahorses, they'll likely give the cb seahorses something they're carrying.
The short answer is: I wouldn't do it again, but it can be done, just expect a lot of cost, time, and potential heartbreak.