Or it could just turn Birmingham into a suburb of London. Quicker access means people can commute and firms may not look then to relocate. It's the same with BHX quicker access to London potentially means it's easier for passengers to get to Heathrow potentially meaning airlines have less need to expand out of Heathrow.
But places like Milton Keynes and Reading are booming, exactly for this reason. Rents in London are sky high, why wouldn't you look to move somewhere cheaper ? Birmingham overall is a poor city, the poorest out of all the big English cities and that is a national disgrace. In the 70s and early 80's Birmingham's economy was richer than London's, so maybe the government have finally realised Birmingham's potential and after 20 years of a booming Manchester which by the way is in the North, it's now time for Birmingham to turn it's economy around for the benefit of its people.
But LHR is at near capacity, so not much room for growth, the reason why they keep chopping and changing routes out of LGW. At the end of the day it will depend on which side of LOndon you live, if you live near Old Oak Common, it may just put BHX into some people's minds instead of a London airport, who knows ?