When the OSSEC agent goes offline, it will stop performing checks and collecting events locally. Therefore, no events are going to be generated regarding FIM, and no further disk space should be consumed. The logs stored at the ossec.log should only be reporting the inability to connect to the server too. Also, the ossec.log files are compressed and rotated daily under /var/ossec/logs/ossec in Linux and C:\Program Files (x86)\ossec-agent\logs in Windows.
If the agent comes back online, then it should perform the syscheck scans back again, and report all file changes comparing the last checksum of the files stored in the database before it went offline with the most recent ones, being able to report which files were modified while the agent was offline.
I hope this helps.