If you cannot get a referral from another author and haven't met an agent at a convention, how likely is it to actually get representation through the query-synopsis-sample route?
Also, how many agents should one plug away at before becoming discouraged with reasonable cause? Assume all agents queried have been researched and represent the category of fiction in question. In this case: Literary Fiction.
Regarding your first question, I unfortunately don't know and I'm unaware of any survey conducted about this type of thing. However, in my opinion I do believe that if you write a book that has publishing viability and you query properly and thoroughly that you will eventually secure representation.
Regarding your second question, I saw somewhere that there are probably about 400-450 reputable literary agents in the United States. While it may not make sense or be cost effective to query all of them, I certainly think that you should be as thorough as possible in your submissions without actually driving yourself crazy. What that specific number is will depend on you.