Yes, It will take up more width. If you vegg a plant too long it will fill up any space. Switch it to 12/12 when it is 6-8 inches tall with a couple of fan leaves. Punch some holes in the milk jug and continually adjust and tie down. You'll be able to manage it, I'm sure. It took my 4 grows before my first one was successful and I got 1/4 oz off a plant in a pc box. You can grow as small or as big as you like.
Your plant can't grow out the sides of the walls but it will reach the lights and burn. LST or putting a wire net (ScROG) over it works great for small spaces. I'm doing some LST on some clones that I put in 12/12 before they were quite rooted. They are miniature plants now. See signature.