Of course they do! Well, at least in one town. Hakone, Japan, which is located outside Tokyo, has Neon Genesis Evangelion electric car changers.
Evangelion is set in Hakone, which is renamed "Tokyo-3" for the anime.
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]
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