Technically, the Lucene parser doesn't allow a true leading wildcard, but the Lucene v3 API does allow you to set the QueryParser.AllowLeadingWildcard bool property when using a PrefixQuery or a WildcardQuery. (Using leading wildcards doesn't work the same as a regular search, as the whole index is scanned for matches.)
This is what I mean when I say the Kentico API doesn't expose that property to developers. You can implement your own search provider to use the Lucene.NET API directly. You just need to know what you're doing. QueryParser doc