Not likely. Most cities now charge an Accommodation Levy, so the Levy charge will not be a total surprise. In winter visitors often come to Yellowknife for three days and stay two nights. A 3% Accommodation Levy would add about $12 to the cost of an average visit for two people. Including airfare, hotel, meals and activities the average three day cost for two people from a southern city like Calgary would be $1,500 to $2,000. So a $12 charge on hotel rooms (@ a 3% Levy) is not likely to be a deal breaker.
For example: Air Canada (2 return fares @ $400 each), Explorer Hotel (2 nights @$195), Meals ($60 per day per person); Excursions (Aurora and dog sled $200 for both); gifts/Souvenirs ($100 each) = $1,630 plus tax.