rush

Yes. As long as you do not accept a bid from a chapter, you are eligible to participate in spring recruitment. If you were to accept a bid you would have to wait till the next Formal recruitment period.

And by "accept a bid," that means that you cannot sign the MRABA at the end of the week before bid day and then turn down the house that you get. You should always maximize your options, but if you are 100% unwilling to give a house a chance after the craziness of recruitment week and decide for yourself if they are really a good fit for you, then you should not list them on your MRABA. (membership recruitment acceptance binding agreement.)

I am never an advocate for intentional single preference (suicide) because I think every house has value and if those members choose you, it's rude to think you are too good for them. But, once you put them on your MRABA, you are bound to them until the next formal recruitment.

Yes, you can go through spring rush, but good luck with that. No one knows what the rules for spring rush are and there is no guarantee that even if you express your interest and do all the right things that you will even be invited to a party. It's an odd system that seems to encourage friends getting friends into their houses rather than giving everyone a chance. There are people on this website who will say "why go through the bother of opening it up and having several parties just to take a handful of people," but I think the answer to that is that if they are that lazy, it's no wonder they have trouble filling their house.