Staying at level 1 via never sleeping is one way. The magic of the PC command console is another. Picking seven major skills that you never touch is another still to stay at level 1.
There are at least a couple quests that require you to sleep. If you want to serve a jail sentence, you need to sleep. The Main Quest requires you to fetch a Daedric artifact from a Daedric Shrine quest. These shrine quests have minimum level requirements and the lowest of them is available at level two.
You never get to see the gear or foes of higher levels. Your foes never get stronger, while you can improve your skills to 100. You are stuck with your starting attributes (boosting by magic notwithstanding). It is easy to become way overpowered. Heck it's easy enough to become overpowered even when you level.
If you're looking for an easy way to make an easy game easier, I guess its viable?
I roleplay deeply enough that I would never ask my character to go without sleep. Never. I find making leisurely progress to level 20 and capping my character there to be perfect. I do so by picking a few major skills to never touch.