I have sprayed leather protector on all my bags before using them--lambskin, caviar leather--all of them. I use a brand called Pedaq, which is very good, but I have also used other kinds. I always ask for the best protector spray at a quality footwear store.
If you're scared, you can always try a small area inside the bag, but I have never had a problem. I have a vintage bag that I have used leather protector and touch-up cream on for a long time--it's black lambskin--and it looks great!
I would still try to avoid the rain, because it just isn't good for leather, period. If you've protected the leather, at least you don't have to worry as much.