I have rehabbed 4 Italian Coach bags, 3 Madisons with caviar leather and cloth linings and 1 Gramercy with textured leather and suede-cloth lining. I have also rehabbed a similar bag that was made in the US during the same era, a Sheridan Glenwood bag with pebbled leather and a cloth lining. The creed patches on all of these bags said that the leather had been "specially treated to retain a new appearance over time."
I didn't want to give them a bath because I was worried about damage so I only used surface cleaning on the 3 Italian Madison bags (Gracie, Royalton, and Carlyle) and they all came out just fine.
I tried surface cleaning the Gramercy, but the suede lining was light-colored and very dirtly. I was able to pull the lining out of the bag and hand-wash it, but it didn't get very clean. I finally decided to give it a bath and it came out looking beautiful with no problems! You can see pics and more information at the link below:
http://forum.purseblog.com/coach/now-cousin-has-come-over-italy-join-family-717893.html#post20462935
The material used for the lining of the Sheridan Glenwood bag is very similar to the lining of the Italian Madison bags. This bag was filty inside and out so I knew that I would have to give it a bath, but it also came out nice and clean with no damage, see pics at the link below:
http://forum.purseblog.com/coach/what-happens-when-you-dunk-bag-shouldnt-get-689911.html#post19266585
In summary, washing an Italian Madison bag is not my first choice but when it appears to be the only option then there is a good chance that you will be able to bathe it without damage, good luck!