Absolutely not the case. Many retail stores will be closed for the holiday but just about every restaurant in town will be open and happy to take your $$$ or swipe your credit card. The restaurants that may close on the 4th of July are the small cafes and sandwich shops located in the business districts that cater primarily to the lunch crowds on workdays.

As for the OP's question, if arriving earlier in the day (pre-1 PM) I would take the Amtrak to Union Station and then a taxi. For the fireworks, use the strollers to go from your hotel to any place that has a clear vantage point of the "airspace" around the Washington Monument and you'll be fine. You do not need to be close... I've watched them from as far away as the south end of DCA and enjoyed them. Expect more crowds than you think...