Thank you everyone for your feedback. I finally got a reply from Intercaribbean from an email I sent them last week, and they said anyone not checking a bag can proceed directly to the gate with no need to go to the front ticketing counter. They did clarify that obviously anyone checking a bag would have to retrieve it from baggage claim and then proceed to the ticket counter to check in, check their luggage, and proceed through security checkpoint.
They requested the booking confirmation numbers for everyone in our group, along with flight number and airline of their flights into SJU. They also asked to clarify who in our group would be checking luggage. They said they’d pass the information along to the San Juan team so they’d know to expect us. They also requested that everyone have their passport info uploaded into their reservation via the IC website in advance in order to expedite and ensure a smooth check in once we arrive in SJU.
They sounded flexible and accommodating, and made a reasonable request that we just not wait til the last minute to get to the gate to check in. Hope this helps anyone else in their own travels!