No, filebeat is only about collecting and shipping logs. It's not about executing arbitrary shell commands. One option would be (optionally with custom script) using a cron-job writing the log-file. Append date to log-file name to create unique filename per run + configure logrotate to delete old files + use filebeat to ship those logs.
Alternatively there is a community-beat (named execbeat) that might help here. But never tried it myself.