Boeing experience not a big plus. All experience is.
At least 2 Airbus 330 transition courses going on right now - and more on the way. Airbus fleet is short of crew and currently far busier than the 777.
Although, where possible, guys are placed on the same "manufacturer" type, ultimately people are put on courses as needs dictate, so you can have a Boeing guy transitioning on A330 and so on.
Basically it's irrelevant what type you're on now.
Recruitment usually say expect an answer within 6 weeks - if not send them an e-mail.
Picu