This is indeed scriptable, here’s an example:
tell application "DEVONagent"
if not (exists search window 1) then error "No search windows are open."
set theSearch to search window 1
if theSearch is searching then error "Search not yet complete."
set theResults to search results of theSearch
set theLinks to ""
repeat with theResult in theResults
set theURL to URL of theResult
set theObjects to scanner objects of theResult
repeat with theObject in theObjects
set theLinks to theLinks & theObject & return
if theLinks is "" then error "No objects found."
set theFile to choose file name default name ((name of theSearch) as string) & ".txt"
set theFile to open for access theFile with write permission
set eof theFile to 0
write (theLinks as string) to theFile
close access theFile
on error error_message number error_number
if the error_number is not -128 then display alert "DEVONagent" message error_message as warning