If the primer is in and locked and working, no fuel should be able to flow into the primer cylinder. That said, it's one of those things that is so cheap and easy that you should fix it right now. Buy the kit on spruce (p/n 05-03637).
Fuel selector off, pull plunger out partway, carefully unscrew the thingy. With a rag in one hand to catch any fuel that might drip out, with the other hand, gently and slowly pull the plunger the rest of the way out. You'll probably discover that the o-rings are chewed up. Use a toothpick or your favorite MIL-STD plastic pokey stick to remove the old ones. Rub some of the lubricant between your fingers, then rub some on the o-rings until they look wet. If they look visibly goopy, you put too much on.
While you're at it, take a look under the panel and inspect the lines that run from the firewall to the primer. Make sure they're not kinked or otherwise damaged, because a leak there can dump gas in your lap.