better chance?

Just because it is considered "bottom tier" does not mean they will give you a bid. Also just because it is "bottom tier" doesn't mean it is less desirable. Some people might not want to be a part of that house, but other people might love it, and think it is the best house for them, meaning it is desirable to them.

Don't go into recruitment thinking of a house as "bottom tier" or "top tier". Form your own opinions on a certain house, and go in with an open mind. Every single house on this campus represents something, and does something for the community. Every single sorority has something to offer, don't just write them off because you have already formed an opinion of a house without even actually meeting the girls in the actual house.

I'm not going to say you have a better chance because you either fit into a house or you don't, but you may have more of an opportunity have this house get to know you. I'm pretty sure less desirable houses during recruitment are allowed to invite more girls back each round because more girls will cut them than other houses.

The short answer is yes. The top houses do massive cuts the first couple of days, whereas the less desirable houses can't be as selective because fewer people want to return. If you "click" with a bottom tier house and can see yourself there, keep putting them high on your list. It's easier to get into a house that has a smaller pool from which to choose. That's just basic math.

Absolutely not. Some of the most desired houses during actual recruitment are consistently ranked poorly on this website. Reputations and rankings on this website are far from true. Go through recruitment and make decisions based on the girls you meet in each house, not what you're read or been told about.