I see that you made your post at 3:31 AM. Maybe you need to switch to decaf!
So are you saying that because ammunition is getting more expensive and harder to find, you are afraid that someone might break into your house just to steal your ammunition? If you really think this is a genuine possibility, you seriously need to rethink your overall home security plan.
If someone breaks into my house and makes it to the room where I keep my guns and ammunition (out of sight but not in a safe), it is highly unlikely they will be leaving my house standing! My five dogs and 10ga shotgun will see to that!
As to your original question, if you would feel more comfortable with your ammunition in a safe, there is no reason (that I can thing of) not to. Just make sure you have one of those de-humidifier thingies in there.
Scott