No. A project based on bunk science is a fraud.

To be clear, space-based boost interception isn't impossible. You can do it. But in practically every case it's inferior to ground-based systems (with space-based early detection). The only case where it has merit is in containing a specific, small adversary with very few missiles, e.g. North Korea or Iran. But even there, a ground-based solution is superior in stealth, numbers and cost.

Space-based missile intercept is a political project. That doesn't mean it won't be done. But it's not something SpaceX is working on, or would work on without first cashing a substantial cheque.