You're right, if your pipe is completely full then you don't have open channel flow. In other words, you can no longer use Manning's equation to model the flow in that pipe. You would have to use either Hazen-Williams or Darcy-Weisbach as you can no longer ignore the pressure term in Bernoulli's equation. As the depth of the water approaches full pipe depth, Manning's is going to become increasingly unreliable. So any air gap, while theoretically would relieve pressure, you can't rely on Manning's alone to model this. Furthermore, even if you model a pipe using pressure equations, models do not reflect the reality of how the pipe was installed anyways. So you shouldn't just say, yes I've provided 10 cm of air gap, therefore the pipe is not pressurized.
That being said, you don't have to ensure open channel flow in a pipe, you could design a system to function near full pipe for a 100-year storm. But as you mentioned in the second part of your question, any nearby manholes or inlets will surcharge and overflow, thus alleviating your pressure differentials (and flooding your site). If there is nothing to alleviate the pressure, the overflow can literally carry away manhole lids or blow them off in spectacular fashion in extreme cases.
Also consider that if your designed pipe is at capacity the amount of additional flow before you see flooding will be very small. Lastly, pressurized pipes are going to have additional stresses on them that will limit their durability.
So you have to consider whatever regulations that you are bound by (minimum pipe size, for example) and economical considerations. You don't want to install a pipe that never exceeds 50% capacity, but I always consider that if you're digging the trench no matter what, it's better to be safe and go with a larger pipe to save yourself a headache later when you don't have enough capacity and you cause flood damage.
The gold standard for modeling all of these situations easily is SWMM which exists as the computational engine in various design softwares. The free EPASWMM is a good place to start if you are researching modeling pipes.