Nah, no need to slow down. Molasses flows faster in winter unless I'm pissed off and swearing. The t and p are distinct. The o vowels in potato get drawn out, and essentially turn into puhtaytuh, unless I'm paying attention and speaking formally but the t and p are separate. I've been annoying my wife trying to make a sentence where it happens, even asked my dad to do it so I could hear him.
I plan to annoy other family and friends tomorrow because it seems weird for something universal enough to end up in an xkcd to not happen at least enough to have encountered it, but because "hot potato" is a game, and a slang term, I've heard it a lot. I can't think of any time there wasn't at least a partial stop between the t and p, with the t being distinct. Plenty of mangling potato until it sounds like a foreign word, but that's a different thing
Maybe it's regional? Gods know the Appalachian dialect is full of some weird quirks.