This is an issue that is resolved by your standard sailing instructions. on page 81 of the rule book they recomend statement 10.4 "a boat starting later then X minutes after her starting signal will be scored did not start This changes rule A4.1
So. If your SI's ommit this proviso. so long as the line is established you could start and sail the proper course. The SI's may also specify qualifiers to finishing. eg. time limit to finish.
If the RC has gone home for the day. a yacht is take their time and report to the RC as soon as possible. I believe that this is in the rule book and it is usally restated in the SI's.