Yes - there is a world of test instruments in the market that are capable of measuring current, voltage and time (Energy = V * I * t) consumed by a Raspberry Pi. Here's one example of such an instrument, and you can find many others by searching the Internet.
You asked about using the GPIO for this measurement. That is rather vague, and would likely be awkward under any set of circumstances, but if you care to edit your question to refine what you had in mind by using GPIO, perhaps you'll get a better answer.
WRT your revised question:
A few USB Power Meters come with Bluetooth - for example. Is it possible to get the power measured by the device over BlueTooth by writing my own Bluetooth program?
Possible? Yes, probably. Straightforward? Probably not. If you'll take the time to actually read the manufacturer's information from the Amazon site, it suggests that they do not publish an API or any specifications that you could use to write your own program.
But the real answer to your question is only available from the manufacturer. I would suggest you post a question about the product on the Amazon website. If the manufacturer provides an "Open" API, then it is likely you can get the measurement data through a program you write. If they don't, you may still be able to get it, but you will have to hack it by studying raw Bluetooth data sent between the device and one of their supported apps (this is likely to require a lot of work).
