Curate, connect, and discover
Cursed? More like uper interesting. Because this could have so easily happened. Mika noticed Seiji purely because of Mikado's name in the anime. In fact, Anri makes a similar remark about knowing him before meeting purely because of his name.
To start off with, there's the whole distance thing. I think Mika wouldn't resort to up and leaving to find Mikado's hometown on the get go. Especially when she probably knows he will be moving to Ikebukuro soon anyways. So I imagine she would resort to cyber stalking for the time being.
Imagine the scene. Mikado is interacting with his group chat friends. There's a cute girly account interacting to him. One would think, "oh that's Izaya pretending to be Kanra". Nope. It's Mika.
Now I don't think Mika would be as intense with Mikado at the start as she was with Seiji. Mostly because distance might have forced her to tamper down her feelings. But once Mikado gets to Ikebukuro, that changes.
Similar to the anime, they bump into each other. But instead of running away screaming, Mika sticks around to show her interest in Mikado. Masaomi acts all super jealous because "no fair, you got a cute girl on your first day" but encourages the idea of Mika sticking around for the city tour.
This gives Mika the chance to follow Mikado home, and when he says "hey want me to keep walking so you get home safe?" She's like "oh no, I think I'll stay at your house" which makes Mikado realise "ok, getting kinda uncomfy here".
Mika then proceeds to make herself at home. Mikado tries to make her tea and be a good host, but he just can't settle down easily with her just, not taking her attention off of him for even a second. He doesn't even have the chance to try and call the police, but he attempts to brush it off because she's not actually being dangerous or harmful towards him.
So like, for the first few archs he's in a perpetual state of "this is fine" as Mika just does not leave him alone, and yet shows her endearing side by genuinely looking out for him.
Cursed Durarara!! AU: Mika gets infatuated with Mikado during the entrance exam
Spoilery ramblings under the cut
Because here is the thing. We know from later in the series that Mika has SCARY knowledge of EVERYTHING. She is a horrifyingly determined and effective stalker.
She would figure out immediately who Mikado is. And would take it upon herself to help him. People are giving the Dollars a bad name? Time to ruin them for Mikado's sake.
It would obviously change a LOT in the series, especially in regards to Celty's head, and the Yagiris role in the plot, and it is hard to pinpoint exactly how things would unfold...
God help Aoba, once he gets involved in the plot. The two of them would have a total weirdo-off over Mikado's attention. (I have the feeling Mika would win)