If my phone is turned off will find my iPhone still work?

If the setting 'Send Last Location' was turned on in find my phone on the device then it should have sent out a last location just before the battery died so at least you would have a rough idea as to where it was.

****, I didn't realise that. Shame that iCloud doesn't save that information for longer, mind you though I suppose if you had lost the phone you would be on the iCloud site ASAP to check.

No the phone cannot be located if it is off or offline. See: If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support

The phone must be powered on and connected to either a known wifi node or have an active cellular data connection for any of the find my iPhone features to work. When off, an iPhone is truly off - all radios (cellular, wifi, BT) powered down.

Remember though that the last location is only shown on the server for 24hrs. After 24hrs since the last location update from the device, all your iCloud account will show is "offline".