Yes.
ESIGN and the various state UETAs legalized e-signatures and e-delivery of documents. Before launching out in this direction, however, you would be wise to have your bank's attorney research any litigation relating to electronic signatures and documents. Of particular interest would be any case where a court threw out a contract or found disclosures (RESPA, flood, Z, etc.) to be unacceptable due to defects in the ESIGN process followed by the lender.
If these loans are to be sold to investors, you will also need to confirm that e-signatures are acceptable to each investor.
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...gone fishing.