Does the trip show as a multi city? If so, the system will likely default to checking the bag to BOS and would require an agent to manually edit the destination to AUS. While it can be done, most agents don’t know how to do this and a supervisor probably won’t override in this case since you are planning on leaving the airport. If you had a LGA-BOS-AUS with simply a long connection in BOS you’d have a valid argument, but DL likely doesn’t sell such a thing without making you split it up into a multi city because of the max domestic connection rule of 4 hrs.

Anyway, I’d plan on having to claim the bag in BOS. If you get lucky and get a great agent who can make it happen consider it a bonus, but I wouldn’t get my hopes up.