A group of legal experts (PDF) and academics have put out a statement on the effects of such a bill:
If enacted, HR 2587 will eliminate the ability of the NLRB and the courts to effectively remedy any discriminatorily motivated decision to transfer work from employees or eliminate their jobs not for legitimate business reasons, but because the employees have engaged in union or other NLRA protected activity. It will also eliminate any meaningful remedy for an employer’s refusal to bargain with a union in circumstances where it is required to do so before transferring or contracting out work performed by workers the union represents.
[T]he impact of HR 2587 would go well beyond overruling the Acting General Counsel’s actions in the Boeing case. If enacted, it will give tacit permission to employers to punish any segment of their workforce that chooses to unionize or to exercise the right to strike by eliminating their jobs. [...] Employers will be able to eliminate lines of work, hire subcontractors, switch jobs to non-union facilities or transfer them out of the country in violation of the NLRA—secure in the knowledge that the Board will be unable to order it to undo those actions.
In short, while House Republicans had the idea of changing the law because of Boeing, they're only too happy to eviscerate protections for all workers in the process. Speaking about the bill, Rep. George Miller asked:
"So, this is my question: Will the Republican leadership work with us to create good jobs in this country and give Americans the opportunity to get ahead in this economy, or will they continue to only help those who are already ahead?" said Miller.
Despite assuming that was a rhetorical question, I'm going to go ahead and answer it "no."