I did pretty much exactly this, bought a bike new in Vancouver, rode it for a week or two (this was at the end of a two year stay in BC) before flying home. Nobody gave it a second glance, and if they had, it wasn’t a new bike any more!
I *guess* if they were being absolute sticklers, they could have proven I had bought it in BC by the ‘Might Riders, Broadway’ sticker on the seat tube, likewise I don’t know if they could check the airlines records to see if you flew out with a bike? You could always claim a friend had flown out before you and taken your bike etc etc.
I think you could assume it would be too much trouble for them to pursue unless you were absolutely blatant about taking a new bike through, you know, by doing something stupid like declaring it to customs 8)
Edit: Airtransat/Canadian Affair were very relaxed and friendly about bikes, even queue jumped me when they saw me having difficulty wheeling my case through the zig-zaggy tensa-barriers at check in. £20/$40 per flight for a bike if I remember right.