Hello
Yes it should work but might I just suggest another option I have been using an fm transmitter that is available from Amazon I use it on iPod nano 5&6 and ipod touch 4g.
I like to listen to audio books around the house and it works suprisingly well through Hi Fi via FM radio so would also work for your Wi-Fi head phones but the head phone transmitter would need to be plugged into your Hi-Fi also works in the car as well there are many other options available of couse your choice.
iPhone Transmitter to FM Radio & Car Charger for iPhone 3G 3Gs 4 iPod Touch 2nd/Second Gen/Generation
Buy new: £7.19 £3.22
22 new from £1.99
Cheap as chips but works well takes its power from ipod.
Regards Alan