Migration of MySQL to SQL Server
MySQL is my area of expertise and SQL Server isn't... but it looks like the answer is you definitely can manage the migration with SSMA on a client PC, but it also appears that both your client machine and the SQL Server need connectivity to the MySQL server.  Reading between the lines, it sounds as if the client machine might use its connection to MySQL to discover the schemata and then something from the server-side components installed on the SQL Server would subsequently connect directly to MySQL to fetch the actual data rather than the data being actually piped through the client machine where you're using SSMA.

To use SSMA, you first must install the SSMA client program on a computer that can access both the source MySQL database and the target instance of SQL Server or SQL Azure. Then, install the MySQL providers (MySQL ODBC 5.1 Driver (trusted)) on the computer that is running SSMA Client Program.
— http://technet.microsoft.com/en-us/library/hh313129.aspx
In addition to installing SSMA, you must also install components on the computer that is running SQL Server. These components include the SSMA extension pack, which supports data migration, and MySQL providers to enable server-to-server connectivity.
— http://technet.microsoft.com/en-us/library/hh313121.aspx