Yes - SSRS has that capability. You can setup subscriptions and schedule those to run with pre-defined parameters (e.g. all divisions, individual users, etc.).
If you install Enterprise Edition - you would also have the ability to use data-driven subscriptions. These would generate the reports based on a query/stored procedure that defines the parameters, the to/cc/bcc users, etc...
Honestly, for something like this SSRS is going to provide a much more flexible solution than using SSIS to generate Excel files. Not only can you provide those files, but you can also provide access directly to the reports - create snapshots to keep multiple copies - create linked reports with fixed parameters (e.g. an All Division report that passes the parameter and is hidden from the user).
And instead of sending the Excel spreadsheets - the users can access SSRS and run the report as needed with whatever parameters they need at that time. Then they can export in whatever format works for them...
One final note: I have often ended up building 2 reports using the same stored procedure as the source, with the same parameters. One of the reports is built as a normal paginated report - with page headers/footers - fully structured for display. The second report is a simple matrix - nothing else - that can then be exported to Excel so that the exported file ends up as a single header row and detail rows, which is easily modified by the users to freeze the column header and add filtering.