mallyh, there are so many different brands of 'floating mop' so it's difficult to tell how effective the one you're considering buying is going to be. I've looked at the claims of similar mops with similar sized batteries (anything from 2000mAh - 2600mAh) and similar sized motors. I suspect that all of them would have difficulty cleaning any floor with hardened on grime.
My advice, go for something like this -
Amazon.com User Recommendation - not that specifically, you may be able to find one cheaper than that closer to home. This is the type of mop that we used at the Dog Rescue, it was great for soaking up spills and I've never used any other mop that could squeeze out as well as that one.
Either way, I wouldn't go for the floating mop.