Speaking from US Gov perspective - if the company is part of a contract (and ~40% of the Gov are contractors), Gov certainly can.
They can put nearly anything (legal) into the RFP/Q. Even if they do not say "give us your BoM", they can wrap it in requirements that in essence delivers the same exact result.
That said, it is Gov mistake to ask for the BoM. They will do little with it in a timely fashion, and lack the expertise to identify risks, and lack the resources to go after it. The best contracts are the ones where the rules and parameters are set for the contractor, (i.e. no untested software, no foreign influence, no this, no that, must have this and that), and auditing of the compliance.