OK Google voice command through bluetooth headset (D.I.Y. Google Home device)
Yes it is possible, it works on my Android 4.4 tablet with a Technika bluetooth speaker and I can say "Ok Google" anywhere in the room and it picks it up, it's pretty sweet! just like an Amazon Echo or Google Home device, just free.. haha. Just make sure "Ok Google anywhere" is turned on in the Google app settings and that your mic option is turned on in the system bluetooth settings and you should have your DIY Google Home/Amazon Echo up and running! I hope this helps  and have a nice day!