Is it possible to operate the MOUSE-E-MOTION Universal Data Logger with normal alkaline batteries? What has to be considered doing so?

Generally speaking, yes. But it is not recommended whatsoever because of the risk of explosion when accidentally an attempt to charge such batteries is made!
If operation with alkaline batteries is wanted nevertheless, e.g. if an extremely long operation span is needed (alkaline batteries usually have a higher capacity than rechargeable ones) or because of no freshly charged batteries are at hand, in any case the possibility to inadvertently trying to charge the batteries should be prevented by covering (e.g. with tape) the connector for the power adapter cable (Battery Recharge).