In Persuasion, is it possible to imagine a similar story in which the genders are reversed?
This question seems to be pointing towards the gender inequalities that existed in Austen's time in society. However, interestingly, I think that the story could have been written with the genders reversed. Marriage was an important undertaking in those times that could only be entered into when the male was able to properly provide for his wife or when the wife was able to bring a fortune to the marriage. Often is was quite common for couples, eagerly in love with each other, to have to wait for a period of years until one of them inherited or found a position that gave them sufficient income to marry. Jane's own sister was precisely in this situation, as she had to wait until her lover gained a parish that would give him enough income to be able to take care of her.
Therefore, marriage was not really a personal decision in the same way as today. There were a number of factors that had to be thought through and a variety of people that needed to be consulted. Families were trying to protect their rich children from marrying to those beneath them (just look at Lady Catherine de Bourgh) and acts of persuasion were very common across both genders.