From personal experience of towing 10 hours up to Canada for 12 years with a pontoon, I have always used the playpen cover. Always make sure it is as tight as possible. If it flaps it will tear itself apart. Towing with it might void the warranty.
I have also towed without a cover on the boat. I do not recommend. It feels like instead of towing a brick you are towing a parachute.
When our cover wore out last year, I replaced it with a tow-able cover built for the boat. It was expensive (+$1,000) but it is beautifully built and should last for the duration of the boat. It is heavy enough that we had a zipper installed to split the cover into two pieces for loading and installing. Keep in mind, that the playpen cover you have is not waterproof at highway speeds in the rain. Found that out the 2nd year of towing to Canada. Our new cover attaches under the decking and does waterproof the boat when stored and towed.