SQL Best Practices Analyzer Rule: Use Of Schema Qualified Tables/Views

SQL BPA says the following:

"One or more objects are referencing tables/views without
specifying a schema! Performance and predictability of the
application may be improved by specifying schema names."

"When SQL Server looks up a table/view without a schema
qualification, it first searches the default schema and then the
'dbo' schema. The default schema corresponds to the current
user for ad-hoc batches, and corresponds to the schema of a
stored procedure when inside one. In either case, SQL Server
incurs an additional runtime cost to verify schema binding of
unqualified objects. Applications are more maintainable and
may observe a slight performance improvement if object
references are schema qualified."

How important is to specify the schame (dbo. in my case) in
stored procedures? Will it really improve performance if I go
and fix each object that is missing "dbo."?

The problem is I have thousands and thousands of them
with no schemas. Before I invest a lot of time fixing them
I am trying to determine if it's really worth it or not?

Thank you