Hi Dave,
Regarding your inquiry, once the sample limit is reached, the manual submissions won't be allowed.
If you have another Cisco product integrated with Threat Grid for example an Email Security Appliance (ESA), if an unknown file is sent for analysis, ThreatGrid will indicate that the file won't be able to upload to File Analysis.
Depending your configuration the ESA will perform different actions, it depends.
You can verify the outcome on that on the message tracking logs.
Cheers,