An empty cart has 8000 weight. So to speak, that's 266 berries he could be potentially carry, which is more or less a fourth team member, thought the cart won't do anything to help you with the mobs. Still, creators need to carry down their own bottles for AD, with time, he'll run out of bottles he would carry in his inventory and be completely useless; you could say he's a mammo build, but it's better to have a WS if he's going melee. On the floors which have Ghost element MvPs, both you and the creator (unless he's mammo) would be useless against them, meaning the sniper would be the only possible attacker for two MvPs, not to mention that the sniper would be open for status alignments since he can't use a shield. Your party has no proficient mobbing class so your party would unnecessarily waste berries on the floors which contain a bunch of normal mobs. Not to mention that in each MvP round, unless you're lucky to have the MvPs separated, two members of your team would have to tank the MvPs, none of the classes being proficient to do that -which translates to more wasted berries-, the best option would be to have the champion and creator tank while the sniper spams his skills.
A party of three, composed of a champ, a sniper and creator -whether he uses the cart for berries or not- would not be able to finish the Endless Tower in the time provided.