You were covered by your employer's worker's comp insurance the first day you began employment with them. The issue here is causation, not legth of service.
Let's say that on your first day on the job, a forklift had run over you at work. Establishing causation for your injuries is obviously a no-brainer. Establishing causation for CTS and other soft tissue injuries is a considerably more complex.
I'm assuming you're fairly new on your job or you wouldn't be asking this question. Whether your CTS is due to your present job can only be established by expert review of your medical findings and the type of work you are doing. Occupational medicine on CTS has advanced considerably in recent years to the point where they can quite accurately pin-point whether a job has caused CTS - even if someone has been doing it for 20 years. Once that happened, the "epidemic" of CTS diagnoses and related claims mysteriously disappeared.
I don't know where you are in the diagnostic process but you should be aware that in the past CTS has been grossly over-diagnosed and many unnecessary surgeries performed. It is still over-diagnosed by some doctors. You should obtain two expert opinions and have a nerve conduction test performed (at a minimum) before accepting a diagnosis of carpal tunnel. If you feel that whatever medical problem you have is due to work, then you need to advise your employer so they can file a claim with their W.C. carrier. There is absolutely no way to predict in advance whether the carrier will accept liability for your claim or not.
