If you run the package manually yes.
If you run the package by a Agent Job no.
If you only want to design and to execute SSIS packages, you do not have to start the SSIS service.
http://support.microsoft.com/kb/942176
http://sqlblog.com/blogs/tibor_karaszi/archive/2009/08/26/do-maintenance-plans-require-ssis.aspx
You need to have SSIS installed so that the components are available for SQL to use, but the SSIS service doesnt need to be started, it is only a management interface service called when connecting to SSIS vis SSMS.