George Redmonds does mention Depledge in his Dictionary of Yorkshire Surnames.
He traces it back to Depleach (Hall) in Cheshire, and notes a Nicholas Deepleache in Ashton under Lyne PRs in 1594. He also comments that it had arrived in Barnsley by then, with a reference to Surnames, DNA and Family History, which he co-authored with Turi King and David Hey.
In this latter book it's said that most pre-1600 references in Cheshire were in Mottram-in-Longdendale, and that Depleach Hall was near Cheadle. The early Barnsley example is dated to 1570.