It is, certainly.
I won't derail the thread with this, it already happens too much. Yes, of course the character of Batman needs a suspension of disbelief. Including Robin asks you to go even deeper though, to the point where suspension can become distraction.
The basic idea of Batman is very real. Plenty of people suffer a tragic event and are shaken into public service of some kind. And if Elon Musk decided to outfit himself with a tactical costume and modified Tesla to fight crime, he could. And die within minutes...but it's possible on some level.
It's very hard to see an adolescent child or teenager in that same context, doing the same things, which is why I suspect most of the time Robin shows up in any medium, Batman's tone usually changes. Which brings me to...
It's not an excuse, it's the main point of my argument. It's too much of a tonal shift, and unless you shift Batman with it, he comes off as even more of a maniac.
Robin, by his nature, is a lighter character, he's meant to be. Making him too dark isn't really the traditional Robin at all. So you have this younger, more colorful and childish character juxtaposed against a surly, acerbic vigilante man. Unless Batman lightens also while dealing with him, it's a complete clash that's hard to accept in any sort of grounded setting.
On top of that, what purpose does he serve in this world? Batman already has a working relationship with an actual cop who he can get information from, investigate clues with, and battle criminals alongside. Do we really need a kid in a circus outfit standing there too? And why wouldn't Gordon have an issue with it himself, there's multiple crimes being committed just by being complicit enough to stand with anybody under 18.
I think the best way to make this work is with a young man OR go the Jason Todd route where Batman making this decision costs this kid his life. Better still, maybe he survives somehow and becomes the Red Hood...then Bruce has to deal with the repercussions of allowing this in the first place.