No, and here's why:
After running two six-hour tests, I can say that it's not the 3DS time that effects berry growth, it is the amount of minutes the berry has been growing while the game is played.
For example, say we plant a Cheri Berry and play the game for six hours. The tree should look like this: (A Cheri Berry's 6 hour stage, as the game has been played for 6 hours.)
If we plant another Cheri Berry and set the time ahead for six hours, the tree would look like this: (A Cheri Berry's 0 hour stage, as the game has been played for 0 hours.)
If we plant yet another Cheri Berry, set the time ahead six hours, and play the game for 3 hours, the tree would look like this: (A Cheri Berry's 0 hour stage, as the game has been played for 3 hours.)
All and all, berry growth time cannot be curbed by changing the 3DS time.
However, changing the 3DS time does reset in-game events, like the Massage in Cyllage City.
Source: Trying this myself and the tests.