Well, considering it's been about 5 years... don't think that's working if that's the plan.
Turkey-- 2.7 million Syrian refugees
Sweden-- 105,000
UK-- less than 10,000
But no, that's not how it works, anyway. They have fled into neighboring nations, and the UN then takes months and months (18+ often) to find them a spot in another nation (and they have no say in the choice).
There will always be those who will just enter some nation illegally, but when they do that they get zero of that "welfare"... so that number doesn't really help the "they are welfare mooch migrants" argument.