Is it important to apply for IP protection prior to applying for government grants such as SBIR/STTR?

It's always a good idea to file for IP protection before any disclosure (confidential or non-confidential). It provides incontrovertible evidence of what you possessed and prevents someone else from beating you to the punch. The better question is whether a provisional will suffice or whether you need a utility application. A good utility will cost almost as much as a utility application. If you cut corners you could end up with a bad surprise.