Yes, kind of. US Tax-Exempt entities directly engaged in "unrelated business activites" can be subject to "unrelated business income tax" or UBIT at the federal

Yes, kind of. US Tax-Exempt entities directly engaged in "unrelated business activites" can be subject to "unrelated business income tax" or UBIT at the federal level. But that's unlikely to deter an agency of the federal government which would not be subject to UBIT.