Depends on how you implement it.
Remember, files on your hard drive are usually marked as deleted (i.e. logical deletion) rather than physically deleted.
You can do the same for your system.
But if you wish to actually delete any and all entries related to that user, then yes, you must go through all tables that reference the user (or rather user id).
Frankly you dont need to search through all tables, since during planning you should know which tables do what.