It might.
My Sprint II did in 2005.
I took a picture at altitude.
I could have probably coaxed it to just under 13K but it was climbing about 25 feet a minute at full power according to the EIS and I'd had enough.
I would think your Sport 2S would do it if the Sprint II with floats did it.
Yes, dress warm. I got some strange looks taking off in a winter coat, hats and gloves in August. It was cold at altitude.