No! Never use a thick, opaque cleaner or conditioner on pebbled leather! I did that once on a non-coach bag and it was a disaster. The white stuff dried in the little valleys between the pebbled bumps and it was impossible to remove. If your bag is trimmed with regular glove-tanned leather, you can use a conditioner like Leather CPR or Apple on the trim.
Since you have already tried wiping it down with clean water and it still isn't satisfactory, I would try Lexol cleaning wipes next. (The cleaner NOT conditioner; I've never tried Lexol conditioner on a pebbled bag.) If you can't find the wipes then you may be able to find the liquid Lexol cleaner in a bottle. You can buy it online, or sometimes at shoe repair shops (or at tack shops for horseback riding.)
The Lexol cleaner is a bit "sudsy" but it is not a thick, opaque liquid like many cleaners and conditioners. But don't let it dry on the bag; wipe the bag down again with clean water and a soft cloth to get rid of any soap residue.
I really like using Leather Therapy Restorer & Conditioner (link below) on my pebbled leather bags. I get it at a local tack shop but it is also available online.
http://www.leathertherapy.com/categories/Equestrian-Products
After I clean the bag, I rub the Therapy oil onto the surface and leave it sit for a few hours or overnight. The next day I gently buff the bag with a soft cloth. It brings back the shine and hides a lot of scratches and worn areas.
Just a warning, the Leather Therapy Restorer & Conditioner oil has a persistent odor, but I don't find it unpleasant (it smells clean to me!)
My next suggestion is more dangerous, but if you still don't feel comfortable carrying the bag after you've tried everything else; then you could try giving it a bath and then using the therapy oil! I once successfully gave a bath to a lined, pebbled leather Glenwood Sheridan bag that was filthy and it came out just fine. But it is not a method that I would recommend lightly. You can see before and after pics of the Sheridan at the link below:
http://forum.purseblog.com/coach/what-happens-when-you-dunk-bag-shouldnt-get-689911.html
What color is your bag? If the corners are just worn, you may need to touch them up with a little permanent acryllic paint. If the bag is black that's pretty easy to do; it gets tricky when you are trying to mix colors to get the perfect match. My glenwood bag is green and I had to use acryllic pain on the corners. They came out "just okay" but it is difficult to match shades of green perfectly.
Good luck with your bag and let us know how it comes out!