It depends what type of power of attorney she has made. If it is an old style Enduring Power of Attorney, your grandfather can use it now without registering it with the court of protection. An EPA only needs to be registered once your grandmother has lost her mental capacity.
If she has made a new style Lasting Power of Attorney, it will need to be registered before it can be used. This can be done now, although she still has capacity. It takes a few months, and cannot be used until registered.
Both forms will allow your grandfather to act in place of your grandmother in respect of her financial affairs just as she would have done herself (except some restrictions on making gifts). He will be required to keep records, and the court of protection website provides good guidance on this.
If, as you say, your grandmother still has mental capacity and you are worried about your grandfather dying before her, it would be worthwhile to ask her if she would like to make a new Lasting Power of Attorney (it is no longer possible to make old style EPAs unfortunately) appointing someone else as an attorney in addition to your grandfather. You can appoint more than one to act 'together and separately'.
In terms of cost, the court of protection provides the forms and guidance on their website for free, but you will need to pay a fee to them to register this new LPA.
In answer to your question, if nothing is done and your grandfather dies, and your grandmother has not appointed an alternative attorney, you would need to make a deputyship application to the court of protection to manage her affairs. This is a much more longwinded and expensive exercise, and carries more restrictions. So if at all possible I would try and get an LPA in place provided she has capacity. If she doesn't unfortunately, deputyship is the only way to go.
Hope this helps a bit, good luck.