Well, let's think about it. A DN100 usually drains the water for half the roof, so maybe 50-70m².
Your gutter should drain the water that heavy rain combined with wind pushes to your front door. We're talking about 2 or 3m², your pavement in front of the door won’t be much larger than that. And it has a slope, I hope. That should be manageable with DN50.
Even heavy rain doesn't suddenly release 50l/m², as if someone poured out a bucket of water. If 120l fall in an hour, that’s 2l per minute, so for 3m² that’s 6l per minute the drain has to carry away.
The problem will rather be that your drainage can’t handle all that, and the water will stand in the pipe after a few minutes. Then it will overflow. This also happens with downpipes, it’s unavoidable.
With 100m² roof area and 50l/m²/h, a 10m² cistern fills up in 2 hours if it was completely empty before. And the emergency overflow is full then too, because the public stormwater drainage is not designed for heavy rain either.