OP - A lot of hair-splitting in many posts above. The bottom line is that if you have GE, there is nothing more you need to do beyond entering your KTN in your passenger profiles. This can be done as to each ticket or, if you are a member of a carrier's FFP, by entering your KTN in your FFP program profile.

You will be eligible for pre-check on any flight where your operating carrier participates in pre-check. Whether you are selected is random, but as others note ought to be pretty close to 100%.