I just became ranker (Florencia rank 10) and started testing the heal amount of potions vs syrups when I noticed something strange. The following are the numbers I got.
Normal White Potion: 1312 hp healed
Ranked White Potion:1365 hp healed
Ranked Condensed White Potion: 1572 hp healed
Now pots have a 20% hp heal difference (Base heal +/- 10%) between the lowest value and the highest value. This means ALL of these numbers come from the exact same calculation and have the same heal range. Meaning there is no bonus for being ranked.
Steph (ranked 2nd) helped me confirm this with the following numbers she obtained
Normal White Pot: 1190
Ranked White Pot: 1396
Normal Slim White: 1292
Ranked Slim White: 1323
Again all within the 20% heal range normally present in potions. This also shows there is no bonus going on.