Yes and no. A Senator, Congressman or other elected official can put in an inquiry with the SSA to have a case reviewed. These cases do tend to get a decision out a little faster. That said, they have absolutely no effect on whether or not the case will be approved. Indeed, there are real limitations as to how far an elected official can go to influence the outcome of a case. This makes sense because you don't want to live in a country where the people who get benefits are only the ones in the good graces of a politician.
This is not to say that there is not a role for elected officials to play. In my experience, the Social Security Administration, like any bureaucracy, can break down. I have seen local office staff refuse to process an appeal for six months and Judges sit on making a decision for over a year. In these instances, a prod from Washington can be helpful to get people moving. Just don't expect for it to make the decision-maker change his or her mind.
If you are concerned with getting a favorable decision, you are much better off speaking with an attorney to try and assist.