Answer: To be honest, I wouldn't recommend it. Peonies need those stems and leaves to function through the growing season in order to stay alive and healthy enough to bloom. The peony season is short but it is glorious, so it would be a shame to lose the plants.
If they have flopped over, as some types are prone to do, in the future you might consider using a "peony hoop" or "peony ring" or other support to keep them up off the ground. For now, you might be able to tie them up and stake them. In order to plant annuals, you might consider widening the planting area and using the peonies as a backdrop. If that's not possible, you might consider moving the peonies to another location. Unfortunately, peonies are best moved in the fall, so that doesn't help much for this year.
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