There are always options. You could carry your entire food supply for the duration of your hike (very impractical, but a few do so), or you could simply hitch into towns along the trail and resupply with what is there. I'm not super familiar with the JMT, but I believe hitching for resupply would always be possible. If there is a post office somewhere, you should be able to find enough food to resupply (grocery stores, gas stations, etc).
I personally believe mailing resupplies detracts from the adventure of the trail. Your body will also have certain cravings that will not be possible to predict in advance. Dealing with post office hours, days closed, etc, can be a massive pain. You're certain to mail too much of some things, too little of others.
In my long distance hiking, I've never mailed a resupply box. Yes, I've certainly had to resupply from crappy gas stations a few times, but I've always gotten along just fine.
The JMT is fairly short and should go by quickly. You're only dealing with a few resupplies. Have you read trip reports and trail journals of folks who have hiked recently? That may be another worthwhile source of information. Here are a few from this past year:
http://www.trailjournals.com/journals/john_muir_trail/2016/
Do you have a target timeframe in which to complete the trail?
