While certainly not an authoritative answer, it appears that an NRSA grant/fellowship would not be considered salary or compensation for the purposes of obligation to pay FICA tax. However, see a relevant IRS Chief Counsel ruling from 2011 for information regarding NRSA and non-NRSA fellowships at:
https://www.irs.gov/pub/irs-wd/1117026.pdf
In particular, see the following citation therein:
"Payments made under NRSA training grants are cost-of-living stipends used to support research training and are not considered salaries; conversely, payments made under non-NRSA research grants are compensation for personal services that the NIH considers to be salaries and wages."