Steve, I'd still do a few hours in Kentucky if I were you. I have a VERY small number of hours gained in Arizona. I did this while I was only 10 or so hours into my UK training.
No, it probably didn't particularly help my triaining. Yes, it made it more expensive. Yes, it was definatley fun and worthwile.
Don't think of any time you do as hours building towards your license, just as a valuable and fun experience. Any time you spend in control of an aircraft is sure to be of some benefit and with family in the US, you're sure to do a lot more flying there in the future so it'll be a good introduction to 'how the other half live'.
One thing I would do is do 4 or 5 hours here first. You'll learn all the basic skills in those first hours and that would also be the time any bad habits will set in and I think it's important to start off properly, i.e. on the syllabus you'll be working to for the rest of your training. The 'training' I had was very.... 'different'.