Can any recent iPhone benefit from the AirPods instant pairing? The W1 chip makes the AirPods and the new Beats headphones instantly pair with an iPhone. Does this work only with the iPhone 7 or would this work with all recent iPhone models as well?

i.e. Does the W1 need a specific client chip to work its pairing magic or would it work the same way with a recent Bluetooth (4?) chip in an iOS device?

(I know the AirPods also work with regular Bluetooth devices, but I'm particularly interested in the instant pairing feature)
Yes, the iPhone 5 and newer running iOS 10 can be paired with headphones equipped with the W1 chip.
From Apple's website:

Beats Solo3 Wireless is ready to go when you are. They instantly set up – just power on and hold near your iPhone – and then simultaneously connect to your Apple Watch, iPad and Mac*.
*Requires iCloud account and macOS Sierra, iOS 10, or watchOS 3