I am pretty sure that you can seek work in the US prior to legally being allowed to be employed here. I say this because some of the foreign postdocs in the labs in my building are doing this. They are legally employed in their current positions, but can't just switch employers. So they are seeking employers willing to sponsor them. But bear in mind that the US spousal visa process takes significantly longer than the UK process (I think). So you should be careful that he doesn't start looking too soon, as his paperwork may take a while.