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.