Yes it is possible for parents to use the same Blackbaud ID for multiple schools, or to connect an existing Blackbaud ID to a school.  When a parent that already has a BBID, for this or another school, is invited they will click on the invitation, just like any other user.  The difference will be, when they are at the "sign up" screen, instead of creating a new BBID, they will select the option at the bottom to "sign in."

Because this BBID is the same account that was previously established, the parent will have the same username and password for both schools.