After Effects Scoreboard Possibility

AE can’t read the text and covert it, as Dave rightly says, you need OCR software for that and I’m not aware of any that would work on moving footage. However you could hook up whatever data source they are using for their graphics into AE. Here’s more about importing data sources into AE;

Work with Data-driven animation

Also, if you are creating a ton of screens it’s worth checking out the Master Properties feature. You can set up Master Properties in the Essential Graphics panel so that comps can be duplicated with a simplified set of parameters to feed the data into.

If you're talking about simply cropping out parts of the scoreboard and repositioning them into your image, then that's relatively simple.

If you're talking about optical character recognition (image to text) then neither After Effects nor any plugins I know of can do that. The only application from Adobe that can do OCR is Acrobat, but that's only in the context of converting scanned PDFs to text. You may be able to get something custom-built (e.g. from a software vendor that does license plate capture software) but it'd be a mountain of work.

Unless you need something that updates in real time across hundreds of videos, it's always easier to just type it in by hand. Unless they have a direct feed from the scoring system that's what all the broadcasters do. Just watch the game and add keyframed values to your text layers as required.