If I had to guess, I'd guess it's slightly less likely if most guests onboard aren't Canadian. Agree that the health requirements for bringing the dog into Canada, if most cruisers are non-Canadian, may put off some illegitimate folks. Anyone flying in, Canadian or not, also have to get their dog past that (but could still succeed) - but as previously stated, if they'll lie about a service dog they may lie about this too.
In countries with very strict animal import laws and strict rules regarding service animals or pets in general (ex Japan) I'd guess the chance is much, much lower. The hurdles to pass are much higher, might even require someone to fake certain certification documents that may be required.
I've seen more stories and pictures about 'service dogs' on HAL than other lines. Not sure if it's confirmation bias, or maybe these folks specifically seeking out HAL, or something specific to how other cruise lines are handling this problem that HAL could maybe learn from. Illegitimate service dogs do a major, major disservice to legitimate service dog teams and can cause additional onboard problems.