Having rowed on the Anacostia for years, I would second Yambag's comments on access to the Anacostia. South of the Pennsylvania Avenue bridge there are limited, if not zero, wading options and the park on the east side of the river is always busy with runners, spin fishermen, soccer games, etc. which would be a royal pain if you were to consider fishing it from the bank.
North of the PA Avenue bridge would be possible if you had a kayak and an access point (again limited due to private boat clubs) from which to launch but the tides get so low north of the PA bridge that I would guess any shad don't travel that far up.
And yes, it is a nasty river but at least it has been improving from where it was 10+ years ago.