Not AFAIK!!! But you could make sure winamp is your default audio player. And I guess you could always try launching each file after completing downlding & add to winamp's library. But better would be moving them to your usual Music folder & then adding them to Winamp.
For fast & easy access, go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here:
Using Library Explore button to access downld folder (click on link) & the folder will open up for you. And then drag & drop them all into your main Music folder. (Hold down the SHIFT key to select all at once!) Then add them to winamp's playlist!
But make sure you share these files back & some of your own ... see
How to Share Folders (click on link)