No. They don't.
The potion of growth states:
When you drink this potion, you gain the "enlarge" effect of the enlarge/reduce spell for 1d4 hours (no concentration required).
If a Wizard casts enlarge/reduce on you, then you will now be experiencing the same magical effect twice, simultaneously It would be no different if two Wizards had cast the same spell on you at the same time.
Since the same game effects don't overlap, the potion of growth does not interact with the enlarge/reduce spell.
Combining Game Effects (p. 252) [...] "Different game features can
affect a target at the same time. But when two or more game features
have the same name, only the effects of one of them -- the
most potent one -- apply while the durations of the effects overlap. [...] Game features include spells, class features, feats, racial traits, monster abilities, and magic items."