No. If you purchase a .org you can put whatever you would like on your site as you are the rightful owner of the domain.
The web address of the Gaar House Museum is: http://www.waynet.org/nonprofit/gaar_mansion.htm
The web address of the Harriet Tubman Organization is: http://www.htorganization.blogspot.com
The web address of the Fiesta Bowl Organization is: http://www.fiestabowl.org
The domain name is the part of the URL of a site that includes the site's name (example: answers) and the suffix indicating what kind of organization it is (.com for commercial). Another example is: name (wikipedia) and suffix (.org for nonprofit organization.)
The web address of the Pittsburgh Jazz Artist Museum Organization is: PittsburghJAM.org
The web address of the Essex Community Heritage Organization is: http://essexny.org
The web address of the Annesdale Snowden Historic District Organization is: www.annesdale.com
The web address of the Flying Tiger Historical Organization Inc is: WWW.FLYINGTIGERHISTORICALORGANIZATIO
The web address of the Sacramento Historical Maritime Educational Organization is: www.dauntlessprivateers.org
The web address of the World Organization Of China Painters is: http://www.theshop.net/wocporg
The web address of the Cumberland Historic Cemetery Organization Inc is: www.chco-online.org/