Not really. They can make inquiries, but there won’t be any effect until after the petition is outside of normal processing time guidelines. Even then, it is negligible in most cases. But it does make one feel like they are doing something by "shaking the tree." Plus everywhere I have read the congressman or senator can’t really expedite the administrative processing. I am just sick of trying and get disappointed. And my biggest worry is to get denied after I waited like over a year.