In short, yes.
Records management laws and rules do allow for records to be kept electronically in addition to, or instead of, physical copies. However, bear in mind that once a record is digitized, it must be accessible and maintained for the full life-cycle of the record and minimum retention period, which can be forever in the case of permanent records.
As a general rule of thumb, you should store the documents at least six months prior to shredding the paper copies. Further, make certain to complete a visual quality control check on all scanned documents to make sure that they are a complete representation of the original.
It is also important to remember that you do not have to scan everything. The initiative to go paperless is not to get rid of all the paper, but instead to decrease the volume of paper that is necessary to manage. Certain records may, or should, be kept in the original physical format based on historical, financial or legal value.