how fast a university receives your score depends on the university to some extends. if they receive scores from ETS electronically (through web) its fastest. I don't remember how long it was, maybe around 3 or 4 days, ets bulletin has the correct info.
but I think you are concerned for reporting general and subject scores together. you can ask the universities to review your application with a copy of your general test score and self report of subject test that you've got by phone until the scores become available and you report them and for the type of schools that you are applying which don't have serious cutoffs its plausible. by this I mean if you look at the top tiers schools, due to huge number of applicants, they don't review incomplete applications. but as you scroll down the top schools everything gets easier and they intend to work with you.