I've never yet had anyone query the size of a carry-on, and an airline which didn't allow suit-carriers as carry-ons might start to worry about a large loss of custom from the business classes. If you do get challenged, a soft bag like a suit carrier can usually be scrunched up to get it in the size-check things, as long as it hasn't been overpacked. Worse comes to worst, you just buy a new bag at the airport which does meet the size requirements - or beg a large plastic carrier from one of the airport shops if you are really feeling the pinch.
As to any wrinkles in the suit after packing, hanging it up overnight will usually sort most/all of that out. Hanging it up in a steamy bathroom can help. Also, many hotels will provide an iron and ironing board free of charge if you ask (never hurts to ask). If you do need to press the suit, don't have the iron too hot, use the iron on the inside of the suit only and put a thin cotton cover (a pillowcase works if you've nothing else) between the iron and the inside of the suit.
Mostly, this is a detail which it could be nice to get right to help your confidence. But I can't remember, in any of the many (non-MD) job interviews I've conducted, that I included suit wrinkles in the assessment.
