I suspect it was the other way around. Hate to admit it, but English (or partial derivations thereof, which eventually became "Scots") was the dominant language in most of southern (Lowland) Scotland from about 1200 on, courtesy of frequent Plantagenet, then Tudor, invasions and occupations. Therefore, it stands to reason that English Jack => Scots Jock.
"Jack" itself has a tradition in Scotland, but as a SURNAME derived from the French name "Jacques". My dear departed gmother bore that surname at birth. It is definitely a Lowlands name and not clan-related.