Whether or not they do, I'm surprised that people think that the Boris wing of the Conservatives will curb immigration even if we leave.
The Tories are very pro business, especially the right wing of it and immigration is good for business.
Labour are too scared to cut immigration for fear of being seen as bigoted.
Either way it won't be cut. Heck Gove even said a few weeks ago immigration could be increased in the short term if we leave in order to offset the financial effects.
The conservatives are just as lax as labour about immigration, only labour are open about it.