Well, if the damage types are any indicator, then the B.A.S.H's attacks would be closer to Normal-type, as they just deal the standard damage type that most enemies deal. Defensively, there are a few enemies that could be considered Water- or Flying-type, and thus ought to be weak to Pikachu's electric attacks, but most of them die in one hit, and the ones that don't are designed specifically around that fact.
Actually, Pikachu should take more damage from a Ground-type attack, since Ground-type moves are actually Pikachu's only weakness, not an immunity! You might be thinking of Flying-types, who are immune to Ground-types.
Either way, though, the electricity resistance is as far as I'm planning to take the whole "type matchup" gimmick. It's just meant to be a fun, easy-to-implement nod to the source material. A fleshed-out element system in a game that's not built around it is usually a bad idea - look at Pokémon Trainer's type matchups from Super Smash Bros. Brawl, where the only significant effect it has is that the already-underpowered Ivysaur gets further nerfed by taking increased damage from fire. I feel like going too far in on the type matchup mechanic would risk unbalancing a bunch of things, since there are only three other elements (liquids, spikes, and fire) that can be nullified by shields, and Electric-type Pokémon don't have any special interactions with Poison- or Fire-type attacks, and I'm not even sure what I would classify spikes as, since it encompasses everything from Spincushions to Castle Eggman's bramble floors.
TL;DR: Pikachu's elemental resistance to electricity is just a cute little nod to his source material, and I don't plan on fleshing it out any more than it already is.