I can't imagine that changing the routing would be an issue - traffic is dynamically routed across the Internet anyway. If SE have a problem at some point, it is more likely to be if the originating IP is being concealed by the use of the VPN.

That said, I find the claimed benefits of these services to be sketchy. If your routing is currently taking you through a dodgy hop, it might help, but bad ping associated with your connection to your ISP's network and just physical distance seem much more common problems, which these services can't help with (as they neither bypass your ISP nor increase the speed of light).