Of course they do! Well, at least in one town. Hakone, Japan, which is located outside Tokyo, has Neon Genesis Evangelion electric car changers.
In Hakone, as part of an Eva campaign and environmental promotion, IT Media reports that Evangelion branded Panasonic Elseev electric charging stations are being rolled out at two locations in the town.
Don't assume these Eva chargers will ever become a nationwide thing. Most likely they won't, but you can still dream.
Other Eva car chargers are also planned:
エヴァンゲリオンデザインの充電スタンドが箱根に出現 [IT Media]
To contact the author of this post, write to bashcraftATkotaku.com or find him on Twitter @Brian_Ashcraft.
Kotaku East is your slice of Asian internet culture, bringing you the latest talking points from Japan, Korea, China and beyond. Tune in every morning from 4am to 8am.