Even if the new pope has the same point of view about gay rights and gay marriage as Pope Benedict, the LGBT community will be effected by the new Pope's stance on the LGBT community and their rights. A more liberal pope might be more accepting, while a conservative pope will continue to make it difficult for the LGBT community.
It's irrational to even try to guess what may come, but judging from the past eighty-million popes, I sincerely doubt that anything different will happen for the LGBT community as a result. Unless a liberal Catholic candidate who is "hip" to such things as "progress" and "change", nothing meaningful will occur in the catholic community.
The Catholics will not change their views on that community regardless who is charge. Scripture is clear on the topic and any divine inspiration otherwise will be the death of the Catholic Church. The LGBT community needs to give up on support from religious groups and press secular governments to respect their right to freedom of religion.
No Pope Benedict's resignation will not change hundreds of years of church teachings or the opinions of the clergy at large. At best the LGBT community will end up having to contend with a pope that ignores them rather than attacking them, but the church's ideals will not change over night.