In the Philosopher's Stone, Olivander states that Voldemort's wand was very powerful.
Also, the Elder Wand is fabled to be the most powerful wand.
I think from these statements that wands are not only tools to channel a wizard's magic, but that they have magical power in themselves which supplements their owner's.
Describing the time Harry and Voldemort's wands connected, Dumbledore says that Harry's wand "imbied some of the power and qualities of Voldemort's wand", implying that wands could also retain wizarding power.
Therefore, I believe that the underage wizard poking the slug with the wand was not really attempting to make the slug grow - they were just randomly poking it, and the slug was growing because a) the wand's own power was being transferred in some random fashion or b) the father's power stored within the wand was being transferred. a.k.a. If the boy were a Muggle, the wand would behave the same way in that situation.
Also consider that if possessing a wand was enough to see magical abilities come to light this way, wands would be given to suspected squibs like Neville to see if any magical ability was present - but this doesn't appear to happen - rather, he is dangled out the window.
Therefore, I think that you cannot draw any conclusions about wands making underage magic more easy to control from that passage.
Final note: I say that wands have their own power, so people may think - then what's stopping Muggles from using that in a much weaker way? My answer to that is that it would be just as random as the kid poking a slug, and not particularly useful for Muggles to allow them to get their own wands. You need to be a wizard to direct the wand, I think.