I think Elinor's first and foremost goal is to avoid seeing Edward, especially with Lucy Steele. So she has to come up with arguments to counter what her mother expects from the trip:

It is very right that you should go to town; I would have every young woman of your condition in life acquainted with the manners and amusements of London.

By saying that Mrs. Jennings will not give them any consequence, I think Elinor is arguing that there will not be as much benefit to them as Mrs. Dashwood thinks there will be. Mrs. Jennings is a nobody, so they won't be invited places, and won't have a chance to partake of the "manners and amusements of London", thus making it less of a desirable plan.