Yes, if you rebuild an index, then the stats for the associated columns do get automatically updated in a manner equivalent to fullscan. (Although if your only goal is to update stats themselves, then doing an update stats with fullscan usually incurs much more overhead than necessary; and unless you have some "unique" situation with some of your queries, the sp_updatestats command is sufficient in most cases to keep your stats current.)

However, to your other point, SQL Server maintains NO statistics for columns that are not part of any index, unless you create your own custom statistics with the "CREATE STATISTICS" command. Check Books Online, etc. for details.