Will my spirituality give me false hope when I am caregiving?

Depends. This depends on the strength of your spirituality. If you doubt yourself this is an area you should seek a mentor for guidance in before you try to discuss it with patients that may depend on you for emotional stability. If you cannot be their rock; then don't try until you can.
It depends. Some people pray for specific outcomes, like cure of illness. They feel that if they're favored by spirit, and they're doing the prayers correctly, the desired outcome must occur. If it doesn't, there's extreme disappointment and shaken faith. While we may be able support others through prayer, we're not in control of specific outcomes. "false hope" might be if we contend that we are in charge.