Using Database Mail there is no way for SQL to directly receive email and SSIS does not inherently have the ability to check for email. So without some external tools that isn't a manner readily available.

However you could probably pull off then run of a package based on a value in a table or the insert of a value. I can think of a couple different ways to accomplish this. One of the easiest would be to create a custom error, create a job to run the package, create an alert to watch for the error and then call the job. Then whatever process that determines that it is time to run the job just execute a RAISERROR with the custom error code and boom job runs.

CEWII