Does the gmail app stop syncing once the "Low on space" message appears? Based on casual observation and anecdotal evidence it appears to me that once the "Low on space" message appears in the status bar the gmail app stops syncing and stops notifying me of new emails. 

Can anyone confirm whether this is the case?
Yes, if you are in fact really low on space then gmail stops syncing. You might also stop receiving SMS's and other data until you have made some space.