A question comes to mind; If you can get the supplies, why not do practical Potions homework in the summer?
THERE'S NO WAND WAVING!! None. At all. Snape's speech back at the start of first freakin' year says so, for crying out loud!
Squibs like Filch and Figg can do potions and use them. Hell, Figg raises Kneazles!
If Harry found out about Arabella, she could get the supplies and he could do as Severus Snape and Lily Evans did; get really good on personal time in summers.
Author's response
I actually agree with your point about doing practical Potions homework in a general sense, but I don't think it would work for Harry.
Like I said in the story, I highly doubt the Dursleys would allow him to do that in their house, and I can't see him being able to go to Mrs. Figg's house to do something like that. Don't forget, she's a Dumbledore plant, so I'm pretty sure that she has her own marching orders in regards to keeping him isolated and ignorant.
Hell, I wouldn't be surprised if the only reason he'd gotten away with leaving the Dursley property in OOTP was because Dung is a piece of shit and wasn't there to keep him from leaving.