No, on Ancestry.com there is no way to search for all records saved to one Member Tree from a given database group or from a particular database.

At least some desktop software can show for whom in a tree a specific source was cited.

Some other tree-hosting sites' software can show to whom in a tree specific sources were cited (for system administrators, not for users). This facilitates consolidating sources within correct repository citations, and some other utility tasks that users don't have access to on the Ancestry.com site either.