Gridcoin is a proof-of-stake coin. Transactions are bundled and signed like any other blockchain, but with proof-of-stake the chance to sign is determined by coin balance and the time since your last block staked rather than by a simple hash race like Bitcoin. The freed-up electricity is encouraged to be directed toward BOINC; if you stake a block and you are also running whitelisted BOINC projects, you will receive bonus amounts of GRC on top of the basic stake reward (which is itself a simple 1.5% annual percentage of your current balance).
So no, BOINC is a software development kit used by distributed computing projects to distribute work and track results. Gridcoin doesn't use BOINC for anything other than bonus reward calculations; the two are symbiotic, not interdependent. If every BOINC project was shut down tomorrow, Gridcoin would work just fine forever as a basic proof-of-stake coin like Blackcoin (which it was forked from) or Peercoin.