pref day

Yes but everyone knows who you are from the precious year. So if they know you cut a house or suicided another they will probably cut you before the second round. I wouldn't risk it

If you attend pref parties and maximize your options then you will get a bid, presuming you don't cuss anyone out or show up naked or something ridiculous (in which case they could leave you off their bid list) That's how the system works - quota is # of girls who filled out a MRABA/# of houses. If all your options meet quota before getting to you on their bid list, you'll still get one of them and whichever house you get will have more than quota, it's called a "quota add" (but you'll never know if you were a quota addition).
So if you go bidless but you had pref parties then obviously you either suicided or dropped completely after pref.

Suiciding is the best way to guarantee you won't be part of the Greek system. On the last day of rush you will most likely attend three parties. The system is set up so that after the parties you rank the three in the order you prefer. If you rank all three you have an excellent chance (almost guaranteed) of getting a bid. If you suicide, which means ranking only one on your list, you have a two in three chance of not getting a bid. The only way you would get a bid is if you are in the top third of the house you suicided. So it's up to you, but if you want to be Greek you'd better not suicide.