I remembered the following quote from The Matrix after answering the recent question about hacking into the Matrix from Zion:
Morpheus: Did Zion send word?
Dozer: No, another ship.
This quote suggests that even if Zion cannot hack into the Matrix directly, it can at least send messages to hoverships at (Matrix) broadcast level. (We don't know for sure if the Nebuchadnezzar was at broadcast level at the time. The ship was close enough to the Matrix to encounter a sentinel; however, it's possible the Nebuchadnezzar had dropped below broadcast level since this conversation occurred just after the Agent training program, which did not involve hacking into the Matrix.)
If Zion can potentially send messages to hoverships at broadcast level, can hoverships send messages to Zion from broadcast level?
Whether or not a hovership can transmit a message to Zion from broadcast level potentially raises another question: if hoverships like the Nebuchadnezzar or the Osiris can transmit a message to Zion from broadcast level, why didn't the crew of the Osiris send their emergency message (about the machine army digging toward Zion, which precipitated the Crisis Meeting in The Matrix Reloaded) directly to Zion instead of utilizing an emergency drop inside the Matrix? Was it just because the Osiris was under attack and couldn't generate enough power to transmit the message so far? Or was it entirely incapable of transmitting a message to Zion from broadcast level?