Married a Romanian Citizen - registering the marriage in Romania?

Hello everyone,

U.S. citizen who got married to a Romanian citizen earlier this year in the United States while on a K-1 visa.  We would like to eventually to move to Romania in a few years perhaps. 


Meanwhile, would there be any benefits to legally registering our marriage in Romania before we got closer to our move states and started applying for visas?  (My wife has not lived in Romania for more than 10 years so she's not familiar with these requirements).  The only reason I ask is because we are visiting family in Los Angeles at the end of the year and I see there is a Romanian consulate there.  I'm not sure of registering a marriage that took place in the U.S. would be one of the services they provide.  Unfortunately the phone number of their website is either not in use or never answered. 

Is this or any other registration possible or even recommended?