Sure. I developed the C# code I posted inside an SSIS Script Task. You'll just need to add a reference to Microsoft.Office.Interop.Excel.dll in the Script Task VSTA Project (what opens when you click Edit Script) to get started.

That said, I would urge you to challenge the piece of the requirement saying this functionality must be available by calling a stored procedure unless they want to move to SQL 2012 where SSIS packages can be securely executed using T-SQL. Kicking off an SSIS package in SQL 2008 R2 and below from within a T-SQL stored procedure implies you'll have to enable xp_cmdshell to be able to call dtexec.exe and that is a dealbreaker in my book. The lesser of the evils would be to create a SQLCLR proc marked for EXTERNAL_ACCESS that will call dtexec.exe.