I don't think that works.
If the Chinese builders are idle, it isn't because they don't have work to complete - the entire crisis is because people basically prepaid for their homes and the builders have yet to complete a lot of them (I think there's a strong implication of embezzlement here). And the Chinese government is desperately trying to find a solution that will get complete homes to the people who have paid for them.
In any case, I don't think a lack of construction companies and/or workers is the problem. It's that local governments are making it impossible to build. We're not going to get more homes built to attacking something other than the bottleneck.