Prednisone has more knocks against it then a front door on a Halloween night.
IMHO yes, you can lose weight while taking the medication. And, no, you don't need to wait to get started. Start with small changes—walk 30 minutes a day, and take charge at a restaurant: Ask for cut vegetables instead of a breadbasket. Ask for the fish to be grilled in sesame or peanut oil. Tell them to hold the cheese, bacon bits and croutons from your salad. Small changes—when you add them all up—can make a big difference.
Good Luck and keep us posted.