When a site column is first created, you can do all the search crawling you want. Full, incremental, doesn’t matter. It won’t show up as a Crawled Property until it’s actually used and there’s data associated with it. Once it has data that’s using it, a simple incremental crawl will pick it up and add it to the Crawled Property listing.
Now that it’s a Crawled Property we can create a Managed Property that maps to it, i.e. create a Metadata property mapping. One thing worth noting when the mapping is created. When you look to select the crawled property to map to the managed property, you’ll see at least two properties with the name of your site column. You’ll want to select the one that begins with “ows_”. After creating the mapping, the Managed Property will be available for you to use, with a caveat.
Caveat: There won’t be any data stored in the search index associated with this new property right away. Content that is associated with property mappings is grabbed by the crawl on a document by document basis. So over time, incremental crawls will eventually get all the content, but the only way to ensure all content is picked up by the new mapping is to do a full crawl.