is it possible to marry a celebrity?

Of course it is.

Of course it's not.

Very unlikely but possible after all Elvis Presley married one of his fans.

Of course it's possible.

There's a thousand of celebrities, actors, actresses, soccer players  musicians ect . . .that they spouses aren't in any kind of industry that perform their job in front of camera and for the society as celebrity, role model or a public image.

The closest example. My favorite music band, Linkin Park. All of them married except the drummer Robert Bourdon. And their spouses aren't into any related industry. They're even so sensitive on protecting their privacy pretty well. Their spouses space. Almost 16 years music involvement and no issue released related to them. Healthy life and relationships.

here from the right: Brad, Mike, Joe, Chester and Rob (this girl is his "now" ex girlfriend from a college they used to go before he become famous, the girl couldn't handle the fame life enough)

In this picture there are Mike and David. Mike Shinoda married with Anna Shinoda after fame. During their second successful studio album "Meteora" on 2003. He climbed on top of the line of celebrity life. Their music blown the music industry, took people's attention, won awards and became a complete public face. And he married a country girl who doesn't have a good connection with cameras.

Yes. Especially now, most are sexing everything and everyone. 

Sure, but why would you want to? If you are married to a celebrity you have to share them with their fans. I would rather be married to someone where I am always most important to them and not have to share.

No unless you are also famous.

Sure it is.  People who aren't "famous" marry celebrities all the time.  In fact, many celebrities say they would prefer to marry someone who isn't in their business.  They want to forget about their "jobs" when they're with loved ones.