Yeah, I didn't catch onto that the first time I saw the episode, but I realized it the second time. You're right.
There's more to it than that. When she, Kenny, and Leona were in kindergarden, they had the job of caring for the Plusle and Minun that were there. Not realizing they didn't like it, Dawn was chasing them around, then picked them up and hugged them. So they shocked her, making her hair stand on end and sparkle. Kenny and Leona commented on this, using the Japanese
onomatopoeia for sparkling, "pika pika". From this, Kenny came up with the Pikari name. Kenny later called her that in front of the whole class, while her hair was still stuck up and sparkling, and so she was embarrassed in front of them all. So that explains her fear of Plusle and Minun, and the nickname she almost drowned Leona over.
Before this episode, I thought for sure the nickname's origin would have something to do with a Pikachu, as I'm sure most others did, but I was completely wrong.