Can duplicate UUID's (GUID's) be generated across multiple devices with the same image?

I am using multiple Raspberry Pis running raspian(Debian) for a project I am working on. I want each Raspberry Pi to have a unique ID so that I can tell them apart on a network.

I have thought that the g++ library <uuid/uuid.h> could be the best way to accomplish this, where the Pi will generate and store a UUID via a daemon program the first time it boots up.

However, I plan to create a stock installation image and load it onto the new raspberry Pi each time I add one to the network. As far as I understand it, UUID generation is partially based off of the system time and because I would be using the same image for all of them, they would probably all have the same system time. (It's possible that they could be booted before they could acquire any sort of internet time.)

How drastically does this affect the uniqueness of the UUID generation?