How many devices can be associated with an Apple ID for Find my iPhone?
I don't think there is any enforced limit for using one account on lots of devices if all you care to do is use Find My Phone. You will run into the 10 device limit if you try to install apps using this ID, but just entering it into iCloud and only turning on FMP (FMi / FMiP ??!) should scale past the limits people normally reach when using one ID for multiple devices.

Even if you get away with this, your users might get confused or wish to use Find My.../iCloud themselves and find you have locked their device

You might want to reach out to your Apple account rep to avoid running into several anti-fraud efforts that prevent this sort of mass scale deployment if you try to use one Apple ID for say the App Store on so many devices. In addition to that specifically being against the licensing terms, you will face delays if and when this account gets locked, so plan to test things out with a small group (say 3-8 devices sharing one ID) as a pilot before you decide how to manage all 100 devices.

There are quite a few MDM packages available, but without knowing your specific situation, it will be hard for you to determine if automating some of the management will be a good investment or if you can just use the Apple Configurator to set up your deices and depend on the end users to manage their Apple ID/iCloud accounts and not mess with your one set up to track all the devices.