Hi Tim.
The short version is, can you get improved ID photos using an extender? Absolutely, when you are aware of its pluses and minuses. I have attached some ID photos that I have taken with the extender including several birds in flight.
I am using the 7d mkii and a 100-400mm mki lens, (got a good savings buying it used and certified on a sale). I also have the Canon 1.4 mkiii extender. I initially was somewhat disappointed with it, especially considering the expense. However, I have learned that it is best used in certain situations and when used properly, it does do a very good job, especially for ID photos. If I wanted professional grade results, then I would spend many more Ducats on one of the really high end lenses. It is sometimes necessary to align the lens(es), camera system to get the sharpest images, but I did not have to do that, my extender mated up with no issues.
While the criticisms of the 1.4 extender are true to an extent at least, I would say that the extender is not without its merits. First of all, to be clear here, I am talking about the Canon 1.4 extender, not an after-market version. I have not tried any after-markets, but they might not do quite as good of a job of playing together with the other Canon equipment and sometimes you lose some of the automatic functions.
You do lose the one stop of light and as the light dims the auto focus does noticeably slow down. Also it is true that the narrower field of view does make it harder to acquire and track birds in flight. With practice, however, you do improve your skills at doing this. Also it does add some extra weight and length and so makes it even harder to avoid excessive camera shake which is also compounded by the additional magnification.
The advantages are that it does give you that extra reach. The 1.4 will actually double your apparent image size. That can be really important if you have a situation where you cannot get close enough using your feet for the best zoom. I have finally settled in on being aware that the extender is useful in good lighting conditions and where you expect to not be able to get up close enough for just the 400mm and crop method. I have found it especially useful for gulls, shorebirds, ducks, waders, etc. It is not really functional if it is overcast or if I am in woodland for instance. It needs lots of light to work well.