That should be approximately correct on a full frame digital camera. Keeping in mind that using a 2x multiplier, even the L series is going to cost you 2 F Stops in shutter speed, and reduce the image quality somewhat.
So stabilization becomes even more critical, not only because you've increased zoom factor by 2x, but you've also lost 2 fstops of shutter speed. So without the extender you might be able to shoot 1/1000s shutter speed with the extender you can now only shoot 1/250s due to lost light from the extender (each F stop cuts shutter speed in half or doubles it). So you can see where if your available light allows for a 1/1000s shutter speed at 500mm, which may make for a nice sharp picture, if you put the doubler in you are effectively trying to take a 1000mm shot at 1/250s to get proper exposure and the image can be significantly degraded from motion blur.
A general rule is handheld you want at least the same shutter speed as your lens focal length, so for 1000mm (500mm + 2x) you want at a bare minimum 1/1000s shutter speed. On a digital camera you can crank up the ISO to gain back some of the shutter speed, but there's no free lunch because you'll reduce image quality in doing so.
It's been a long time since I looked at big zoom point and shoot cameras but Nikon now has a 125x optical zoom point and shoot for around $1k, the Coolpix P1000. The photos actually look pretty amazing, but you'd need a pretty serious rig I'd think to stabilize it well at that zoom level. If you had enough tripod to keep it solid I'd think facial features would be easy at 150m