Yes, there would. Don't forget, the UK and Europe get shafted on distribution and prices every bit as much as we do ever here. That's not anecdotal evidence; I lived over there and had firsthand experience of it. It isn't always the same items but it is just as bad. The UK and parts of Europe also have a much larger market made up of grey market and secondhand importers, some of whom on occasion use stores like BBTS essentially as wholesalers, because they don't have the same protectionist import taxes we have here. This move would drive those small and medium size businesses out of business, and would be sure to raise a stink with them.
I have no idea what proportion of BBTS, or any other online retailer's, sales are made up of overseas customers, but given the amount ordered by the European stores and the fact that pretty much every member of boards like this orders direct from them, I'd say it isn't insignificant. I also think you're underestimating the amount of pull BBTS specifically has with Hasbro; look at the number of exclusive and shared exclusive items they get on a regular basis. Their online order was high enough to entice Hasbro to produce the entire Dark Energon series after Walmart got cold feet. They aren't a small retailer, and they would definitely raise a stink about a mandate that would cut into their market share as this would. Enough to get Hasbro to back down? Maybe not, but then there are the other online stores. Easy enough for Hasbro to bully a small store that sells only through eBay, but a bit more difficult for the really popular stores with their own websites.
There's also the fact that it would be ineffectual at that level; Robotkingdom, for instance, are Hong Kong based, so it would be up to Hasbro Asia to do something. Plus, when have you ever known Hasbro US (or any American toy company, other than PLaymates apparently - Lego are not American) to give a slag about what's happening in the rest of the world?
It's a move that's anti-fan, anti-retailer, and ultimately boneheadedly anti-Hasbro. But if it does go through, it'd be enough for me to throw up my hands, buy Fortress Maximus, and retire to live out the rest of my days in peace with my completed collection. But it isn't going to happen.