Want to make sure not to conflate the two issues at hand...
1) Terminal C TSA (or any other terminal) will allow you through security as long as you have a valid boarding pass for travel that day out of BOS.
2) In any US airport, they will only let you through if you have PreCheck printed on your boarding pass. Flashing your Global Entry credentials will do no good. See TSA site as well:
https://www.tsa.gov/precheck/faq
Can I access the TSA Pre✓® lane by showing my Global Entry, NEXUS, or SENTRI card or TSA Pre✓® approval letter?
No. To receive TSA Pre✓®, you must include your known traveler number in the appropriate field of your airline reservation, and the TSA Pre✓® indicator must be visible on your boarding pass and embedded in the barcode. You will not be eligible to access the TSA Pre✓® lane by presenting a trusted traveler card, TSA approval letter, or other documentation.