As someone coming to town, both as a DVC member, and someone that will be working during the games and the Home Run Derby, I would guess it will be busy. The players for this game often bring their families, so I picture days full of semi-famous families running around the park, plus the thousands of fans that will come from around the nation for the games.
There will be a FanFest going on too, which I would guess will be at the Anaheim Convention Center. It will have old-timers there, besides tons of fans. All in proximity of the parks.
That said, I booked my room at the GCV no problem this past week, and it's not even my home DVC resort. That would make me guess as of yet, there's no rush to get there.