Can you fish to supplement your food. The simple answer is yes.
The complicated answer is......every state requires a license. Out of state licenses can be prohibitively expensive. Getting caught fishing with out one is even more expensive. They can confiscate your gear, leave you with a hefty fine and in even a court date. Then there are the regulations. Size limits, what species can and can't be kept, seasons on what fish you can catch and when, and then in some areas there are even more specific regulations such as fly fishing only, no live bait allowed areas, and again further divided up regulations such as certain stretches of streams/rivers that can or can't be fished and which can be very confusing to follow if you're not familiar with the area. Lakes can also be divided up into sections restricting what, how many, where you can fish and with what. For example...Montana has 102 page book on fishing regulations, and it gets pretty in depth.
Then if you do catch one, there's the cleaning and preserving of it. If you are in bear country extra considerations must be taken.
And this is coming from someone that's fished all his life, all over the country. But when I fish out of state, the trip is a vacation to go fish. I study the regulations beforehand and sometimes hire a local guide. When traveling and living out of my vehicle, I don't think it's a practical way to obtain food, and certainly not the cheapest way. Easier to buy a few pieces from the market when you get the craving.
And remember, you can literally fish 8 hours a day, several days in a row and never catch a single fish. Or only catch ones you aren't allowed to keep. By the time you factor in your license, time, gear, travel, it's a very expensive meal. In some areas, you wouldn't even want to eat the fish you catch, depending on the body of water they came from. Lots of areas have high mercury, in turn, gets into the fish, that then gets into you. I've fished in areas where they advise eating no more than a fish or two a month from certain bodies of water.