Unfortunately there is no copyright on the name Audubon. Many different organizations and businesses call themselves Audubon and they are not related. Each would have a different policy. You have to use the words before and after Audubon to find the specific organization you are asking about.

This is an absolute and definite maybe. The website for the Audubon Society of Rhode Island describes a resounding "no letterboxing" policy. However, thethreecs, a member here on Atlas Quest who is currently employed by the Massachusetts Audubon says they have no statewide policy about letterboxing and each Audubon location is autonomous and some allow it while other don't.

Special note: The Caratunk Refuge in Seekonk, MA is under the jurisdiction of the RI Audubon Society and is subject to the "not allowed" policy despite its location in MA.

So ask before you plant. Rhode Island Audubon locations seem to not allow it while Massachusetts Audubon locations may or may not allow it. The policies of other states are unknown at this point.

Original source of Massachusetts policy (posted to the Premium Members Only board and therefore only accessible to premium members)
Audubon Society of Rhode Island