Lightsquared was going to pay some of the upfront costs, but most of the contract was down the road with Lightsquared sharing in the operating costs. PCmag has an article with some of the details here http://www.pcmag.com/article2/0,2817,2389312,00.asp
Whether or not it would have sped up the rollout... Sprint has no buildout requirements, so the only thing keeping them to their aggressive rollout is the cost of losing customers. If Lightsquared was in the picture, they might have had some buildout requirements that were part of them being approved to use their spectrum. That might have forced them to hold the contractors to the planned buildout rate, and sped it up or at least kept it on the schedule that Sprint is currently using.
As far as Lightsquared being back or bankrupt. They are in bankrupcy protection, but there is some support to try to swap their spectrum with some DoD spectrum, so they can still deploy their network. Basically their entire future depends on that spectrum swap.