Currently the only way to check is by using the VizAlerts logs in ..\VizAlerts\logs. Two things to keep in mind:
1) VizAlerts as installed only keeps ~7 days worth of logs, if you want more then you’ll need to change a bit of code.
2) The VizAlerts logs were initially designed to support admins in identifying issues, not so much tracking which emails were sent out and when. If you’re looking to do something like graph what emails were sent by what alerts at what times then you’d need to do some log parsing. At https://github.com/tableau/VizAlerts <https://github.com/tableau/VizAlerts> we do have an enhancement request for improved logging, so it’s a known issue.