if the information is incomplete for SAP processes in general, then SAP will not allow to save.
if the information is sufficient for SAP but not for your designed processes, then you might create problems in follow on processes when you use the material despite of its incompleteness.
e.g. if you did not enter a purchasing value key, then you do not have the defaults from this key when you create a purchase order, so you either need to maintain more fields manually or you just forget to maintain them and you cannot send reminders, and SAP cannot close the PO automatically with the receipt as it does not know any tolerances for over and underdeliveries.
if you missed to enter a inspection type, then a material is posted into unrestricted stock without having been analyzed after the receipt.
So you better control the completeness and prevent the usage until it is completely maintained by setting of a material status.