I hadn't thought about the immersion factor...
It may take away from immersion, but I've played several games displaying your score, and it didn't affect me until I was trying to get a high-score having finished the game.
High-scores are pretty much a way to make a game repayable IMO.
I was requesting it because I had a really hard time knowing what contributes the most/least to the score.
Ex: I just got 6000-ish points in a very combat oriented run.
The run before that I got 2000-ish with about the same tactic.
Both times I died at around the time those programmers show up.(Death on both runs: something blows up, no cover left , attempt to flee a huge swarm of bots while losing everything!)
When did the score increase that much? I know the reason of my deaths, but I have no idea what made the difference- was it the additional machines exploded, just plain more destruction, or are programmers worth many points? Does overkill damage contribute to score? Etc.
In any case, I think knowing your exact score at any given time could change the experience for the worse. As I see it, score is currently somewhat overemphasized because your route through the world is more linear, whereas in the future stories will (optionally) play a much greater role in the experience.
Once the game is done, and the player knows all the possibilities, I bet he'll try maxing his score.(Like most games with a score actually)
You could make it a toggle option which is only available if you finish the game once. (I haven't managed that yet, need to play more :p)
The main problem I have right now is the "BAM YOU DIED, HERE IS A SCORE WHICH YOU SEE FOR THE FIRST TIME!" feeling you get.