It really depends on the school and the chapter. Some places being a junior won't matter, but at a lot of places it raises a lot of red flags.
If I had to guess (given the culture of Southern Fraternity life, and even just at other big greek schools like my own) @ LSU, it probably matters. Being a sophomore is likely not an automatic deal breaker, but being a junior is.
In my chapter at a more northerly school, we routinely rushed sophomores, if they were an excellent fit, but didn't give them quite the benefit of the doubt we gave freshmen. We had one junior go through rush while I was in the chapter, and he really didn't have a chance. There were plenty of questions: why now? how is he going to mesh with his pledge brothers? how is going to handle having to do study hours and the other things required during pledge semester, when he's already had 2 years on his own? what about his other friends, are we essentially a free party for them? What happens when he turns 21, is he just going to ditch his pledge class? What is he really going to bring to the house and his pledge class in only 2 years?
Those were the types of things we looked at. In the end, the guy was a jackass so we didn't have to worry about it, but the experience and going through those types of questions pretty much made everyone's minds up not to rush juniors in the future.
If you're a sophomore, then certainly rush, but if you're a junior, then you better have some good reasons and be able to answer some of the questions posed above.
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"I address the haters and underestimaters, then ride up on 'em like they escalators"
- Abraham Lincoln
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