Does Performance Analysis for SQL Server supports SQL Server 2008 SP1 build 10.00.1798 (cumulative update 4)?
Yes, this SQL Server build is supported.
It is supported within Performance Analysis version 22.214.171.124, even if it is not explicit mentioned in the Release Notes.
Performance Analysis contains an SQL Server patch level auto detection engine. With this engine PA is able to discover the patch level of the SQL Server instance and adjust itself to enable the connection to the instance.