Perhaps I don't understand, but mpirun has no problem being executed using the "at" command. Perhaps the problem is that you don't have permission for "at"? Per the man page:
The superuser may use these commands in any case. For other users, permission to use at is determined by the files /etc/at.allow and
If the file /etc/at.allow exists, only usernames mentioned in it are allowed to use at.
If /etc/at.allow does not exist, /etc/at.deny is checked, every username not mentioned in it is then allowed to use at.
If neither exists, only the superuser is allowed use of at.
An empty /etc/at.deny means that every user is allowed use these commands, this is the default configuration.
You also might check to see what directory mpirun is executed from when "at" actually runs, and that the path to both mpirun and your executable are correct for that location.