Per my test, after we add Property Key and index it through PowerShell as shown below:
$web = Get-SPWeb http://sp13:36043
$web.AllProperties["SiteJulie"] = "JulieTest"
$web.IndexedPropertyKeys.Add("SiteJulie")
$web.Update()
Then run full or incremental crawl, we can see the crawled property from the search service application:
After that, we can create Managed Property that maps to the crawled property.
Also, if the property value is updated later, it is sufficient to run an incremental crawl on the items which have been newly created or modified since the last crawl, without re-index.
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