I'm not super-sure about how much DC could get from a program like that. The London congestion pricing program ends up increasing their transportation system's total funding by only ~3%. The various NYC proposals have all eventually been modeled around the same, I think. Cost to administer is roughly 25% of revenue brought in.

The money would obviously help, but only if it doesn't increase downstream costs like even lower office-worker spending downtown.

Now congestion pricing is good if your goal is to reduce traffic at peak times, but that's sort of a separate issue.