No, reading usb drives should have more worse effect then on any other electronics that is powered up. Flash drives do have a limited number of write cycles but usually this number is much higher then you'll need in you life time.
Since reads don't wear down USB drives, then you should always be able to read them.
Siliconvideo is correct, reading a flash drive doesn't wear it out.
But you should be aware that there IS a lifetime issue with data stored on a flash drive. Data is stored as a series of static charges - over time those charges will dissipate and your data will evaporate. The papers I read on the subject suggest that something like 10 years is a reasonable expectation for data to be retained before this starts to become an issue.