Yes. A car dispatch fee (pick-up fee) will apply. Please inquire with each taxi company with regards to the amounts for the fees they charge.
In addition, taxi companies that have introduced a slip system do not charge a pick-up fee, but the distance and fare during pick-up is treated as the first ride by turning the meter during pick-up. * However, there is an upper limit.
Tokyo
・Daiwa Motor Transportation (Please refer to the pick-up fee shown)
https://www.daiwaj.com/service/taxi/price/
・Kokusai motorcars (Please refer to the pick-up fee shown)
https://www.km-taxi.tokyo/call/
・Taxi Kotobuki (Please refer to the pick-up fee shown)
http://www.taxi-kotobuki.co.jp/ryokin.html
Aichi
・Meitetsu Taxi Holdings (Please refer to the pick-up fee shown)
https://www.meitaku.co.jp/taxi/unchin.html