Yes, it will, and bomb-proof spearmint is especially good at standing in moisture. It will run, which makes for nice mowing around the edges. Apple mint has much more felted leaves and needs better air circulation. My colony of apple mint is on a sunny, windswept hillside.

I've found that the dry clay locations I've planted mint have kept it from spreading wildly. In fact, it spreads very slowly there. But it likes the moist or average moist clay locations I've put it.

I would pick one mint variety to try in the location rather than planting multiple varieties.

FataMorgana