Test results ...
Okay, this isn't ground breaking, just some results from the average testing necessary to determine what you can expect from your SONY A100 Alpha.
First off: f/8 is the crossover for autofocus. Par for most digitals. As one my expect, using a 2x Teleconverter (T/C) pretty well knocks out the autofocus when using the 70-300mm f/4-5.6, when it is ranged from 210-300mm, because the light is reduced to f/8.
Using a 1.4x T/C restores AF because the light is coming is improved to f/6.3, which is just enough to get the job done, as it is with other manufacturers. Like I said, nothing earth-shattering, just proven.
Unfortunately, at that aperature, indoors, you need a bit more of a light source than the pop-up flash can provide at five feet. Even the external flash (HVL-F56AM) is hard-pressed to cough up enough light, but it gets close. Things to remember when using these combinations.
Here are a series of shots using some maximum settings to get an image with the T/C attached.
The same lens settings w/o the T/C attached
The A100 selected f/5.6 - 1/125 sec. - ISO-400, so the resulting image is darker.
Personally, I preferred these manual settings @ 5500K, which delivered a richer, more "natural" image, like it appears with the lighting in the room.
With a better lens (f/2.8), the image is improved. Admittedly this was with a Canon 20D, but the glass is the real magic.
Obviously, the 70-300mm-style lens is much better outdoors, in daylight, than indoors, mainly due to the fact that the minimum focus is about five feet. Indoors, that takes a lot of room to try and frame an image, even at 70mm (which effectively 105mm after the digital cropping factor (1.5x)). With the 1.4x T/C, that makes it an effective 147mm shot at the low end and 630mm at the long one.
So when you pop on the 1.4x you are better than doubling your "effective" lens focal length (compared to a the same lens on a 35mm-film camera) and still maintaining autofocus. That's not bad. The SONY A100 maintains a reasonable autofocus, even in the subdued lighting. The loss of light is unavoidable with a T/C and the reason behind these shots was to demonstrate just how much is lost, but how you are still able to acheive a good focus and stable image.