I got a bid as a junior in an SEC school. I would say I was at somewhat of a disadvantage because I was cut from many of the houses after just the first round, but I did make it out with a bid to a group I'm very happy with! And I can think of at least three other juniors in my pledge class.
A girl I met who rushed as a sophomore, however, was cut before the final round--so she didn't get a bid. Therefore, I'd say class standing has some impact... but it is not the ONLY thing they look at. They will be harsher with you because you're a junior, but if you do well during recruitment and have a high GPA, you should get a bid somewhere. You may even beat out a sophomore or freshman.
I wouldn't necessarily count on getting a bid with "XYZ," though. It depends on your campus, but when I went through as a junior, it seemed like my sorority chose me rather than the other way around.
I ended up very happy! So just keep an open mind.