No, not at all...the stats are held on the actual cleaning tape itself. Even if you somehow managed to do this within BE, the tape only has a finite amount of runs available...at 25 or whatever it is, the tape becomes useless.
Your screenshot is missing context. Craig is correct in that the cleaning cartridge does keep it's own internal count. But, BE also keeps a count in the BE database. This can be reset. But, as Craig stated, a cleaning cartridge has a finite life.