I’ve done 340 miles in 60 hours (including a couple of short rest breaks) during the Missouri River 340 Race, but it wasn’t a lot of fun, and not something I’d recommend without training or significant experience. You’ll need a support team for food/water resupplies because you won’t want to be carrying any extra weight (especially if you have portages around dams). I don’t know that river, but you’ll need to cover almost 100 miles per day which is going to take a fairly significant caloric intake at a steady rate. Think constant snacking or many smaller meals versus breakfast, lunch, and dinner.
To maximize daylight you’ll want to schedule your attempt near the summer solstice, but unfortunately that will mean higher temperatures and sun exposure. You’ll need to be very careful how you dress. You’ll be hot during the day and cool in the evenings. Sunburn and exposure have knocked many good paddlers out of endurance events.
Yes, I’m sure it can be done, but you better do your homework and know every facet of your course including portages, resupply points, etc. Good luck!