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

The primary rule with protecting IP, that is, patents, is to not publicly disclose your proprietary information/invention before you file a patent application. If your invention is substantially complete, you can file a provisional patent application and then you need not worry about disclosing anything to anyone that is covered/disclosed within your provisional patent application. If you disclose first, then you can get into legal quicksand - was it/not a public disclosure, did you/not disclose to third parties, was it/not considered private information, whatever - filing a provisional application first effectively removes any public disclosure problems.