[JonathonW]

If that's how the contract's written, yes.

IME (and I've worked on a number of federally funded projects at this point, both in and out of academia), these contracts typically get written such that the institution retains all rights to the software, but grants the US government unlimited rights to use the software.

(I will note that it's also not unheard of for these contracts to stipulate that the end product becomes open source-- software I've worked on that was funded through DARPA is up on GitHub, for example.)