Danny Finkelstein thinks so. Noting that Blair had said that modern politics is more a matter of Open vs Closed than Left vs Right:
And then I asked which politicians on the right he regarded as on his side, the open side, of the new argument. He replied:“
I think you can see the Republicans in the US who are on the pro-immigration side of the debate, on the pro-free-trade side, the Americans who are Democrats but protectionist. I think the thing that has come home to me most since leaving office is just the speed at which the world is opening up.
Full interview - largely on Blair and his Faith Foundation - here.