Short answer - probably. Slightly longer answer - I'm actually not sure. It'd have to be set really high, and even then, collection might be an issue.
Let's deal with the amount of the fine first. It'd need to be huge, enough to erase the economic benefit of the rental activity, and then some to deter the attempt because the odds are you still won't get caught. Let's say you do something ridiculous like $50k per occurrence, just to keep this moving.
Anyone serious about doing this is going to restructure such that the fine becomes difficult to collect. Make the city spend $100k to get $50k from you. Individual property owner X creates Property Management Company Y. X leases property to Y. Y does all of the business on AirBNB. Y gets fined, goes to court, judgment sticks, so Y declares BK and dissolves. X leases to company Z, rinse and repeat. Literally a shell game until the city gives up or something bigger comes down, who knows, but point is you can frustrate enforcement efforts in protest if you're so motivated.
Then there's the question of the fine. I really don't know if there's a constitutional argument on an excessive fine or not in this case, but I think the Supreme Court left the door open on that. Kelco might be the case.
Please keep in mind, I'm just being an armchair analyst here. I'd be pissed off if my neighbor's house suddenly became a revolving door of loud campers. I'm just not realistically sure what could legally be done about it beyond restricting short term rentals. But then I'd just have weekly campers instead of daily.
Couldn't you just set an extremely high penalty for breaking the law and then only enforce it against the most egregious offenders, as a deterrent?