Yes. It is a safe to say that Jonathan Ive has studied the work of Dieter Rams. When it comes to industrial design, Dieter Rams is one of the greats. There is nothing wrong with being inspired by him. It is important to note that this inspiration goes beyond the industrial design of Apple's hardware. For example, it is widely agreed that the iPhone's calculator app is based on the Braun ET66 calculator, designed Rams: http://barryborsboom.files.wordpress.com/2008/10/172_721-ram...
The calculator app doesn't look like that now, though, even though it's clearly inspired by it. I believe I have seen that design on the iPhone before, but when I bought my 3G two years ago, I believe the buttons were square and the '='-button was bigger. Did it look like that in the original iPhone?