FrogReaver
As long as i get to be the frog
Not really - improved divine smite adds to all melee weapon attacks, not just smites. The spell slot still only adds 2d8.
If all spells gained an extra die of damage at levels 5, 11, and 17 regardless of which (if any) spell slot was used, that would be equivalent. But I wouldn't want to do that, since casters are already plenty powerful.
Improved divine smite adds a total of 2d8 when using a spell slot to divine smite.