Hi Lara.
Thanks for your interest in our plugin suite.
I’m unfamiliar with Blackbaud, but I’d say no, not via an API.
However, if you can turn that data into a valid iCal feed, then you could use our iCal Importer (soon to be replaced by an even better Event Aggregator). Or if you can turn that data into CSVs, you could import using CSV, which is included free in The Events Calendar core/free plugin.
Note that PRO isn’t required for either of these import types (iCal or CSV), but, of course, it adds great functionality too!
Last but not least, we have a pretty great Refund Policy so you can buy one or many of our add-ons and thoroughly test them.
Let me know if you have any follow-up questions.