A little bit, but they shouldn't make a massive difference to your iPhone battery life. When you're connected normally to your iPhone (as opposed to using AirPlay, which uses more power) your Bluetooth connection will use some battery power.
However, Bluetooth is designed to be a low power technology so even all-day streaming shouldn't do much damage to your battery life. AirPlay is more demanding because it uses the more power-hungry Wi-Fi to transmit and receive data.
The bigger drain on your battery isn't your AirPods connection: it's streaming music from the internet to your phone, especially when you're using mobile data rather than Wi-Fi.
If you're finding that you're only really listening to music and your battery isn't lasting all day, you might want to use your music app's offline mode and download the music to your phone rather than stream it when you're out and about.