Hi Steve.
Your assumption is correct – adding 001 will work for both texting and calling between US cell phones located in Europe (this goes for contacting the US from Europe as well). Most likely using 00 will present a problem when back in the US. There is an alternative to using 00: the plus sign. So instead of storing 001 in your cell phone memory you may also use +1 which does the same thing. Moreover, +1 might still work when returning to the US.
I will explain this a bit. Adding 001 means you are dialing out of the European country you are in back to the US. The call or text is then redirected to wherever the person you are trying to reach is located. 00 is called an IDD or International Direct Dial code. However, other countries use different IDD codes to dial internationally. The US for example uses 011. The plus sign replaces any IDD code. Of course, using +1 while in the US does not make sense since you are dialing nationally, but many wireless carriers today simply ignore the plus sign in this situation.