Hi DaisyLuck,
I think the only answer anyone can give here is "maybe".
The BRC standard is very clear that in general GFSI certification or an audit is required, unless the supplier has been assessed as low risk.
I suppose there is a slim possibility that the government inspection process would satisfy the 2nd/3rd party audit requirement, but only if the scope covered the areas required under clause 3.5.1.2 and you'd probably be expected to have a full copy of the corresponding audit report to be able to review.
Even if you determine the supplier is low risk you'd still be expected to assess via a questionnaire, and verify their traceability systems at least very three years.