Unless you have some obstruction down below the rod holder that is preventing the butt of the rod from swinging down, yeah, odds are, you should still be able to set the hook this way. Once the rod is out of the barrel of the holder, it's free to swivel upright at almost 360 degrees. Again, with the hook of my fingers I'd lift and yank at the same time. Once you get the rod past that black plastic barrel, you should be free to get the rod in the vertical position. Hard to explain, but easy enough to follow once you see or do it.

If I had a boat configured this way, I'd look in to those swiveling rod holders that the Really Big One uses on his boats. Sorry, but I don't recall the names of them. You can still swivel the rod holder out and away from the boat, yet keeping the rod tip pointing (mostly) down river. If the baits (Kwikies) are staggered, you can get those rods pretty close together without tangling gear....until a fish hits, but at that point, it's all fun any ways! I love goat rodeos!