I personally wouldn't say so, no. I don't really think the 4gb is a good option. I appreciate he's only 8, but he's only going to get older and more savvy.
On Xbox Live, playable demos of the latest games are often bigger than 1gb in size, I downloaded one the other day which was 1.6gb. There are also loads of great Xbox Live Arcade games available, which are smaller, but still often hundreds of Mb. With some of these Xbox Live downloads, and game saves and other data, 4gb will be full in no time.
If you buy the bigger version you can also install games to the HDD. Some games are noticeably better when you can install at least part of the data to your hard drive. Battlefield 3 isn't a game your son is likely to be playing any time soon, but it needs a 1.5gb install to have the best graphical performance. If other games follow this path, then this will be an issue for those with 4gb consoles. Also, when a game is installed the disk drive isn't constantly running, so the console is quieter.
In general, I think you may find the 4gb version a false economy, as you'll end up shelling out for the bigger hard drive in no time at all. But if the Best Buy price is really good, it may be cheaper to buy the 4gb then add an HDD?