Clicking is a hardware issue: the heads can't read for what ever reason.
If you need the data - send it out.
If you would only 'like to get the data' do as you wish but do not hold high expectations.
Often it's a result of the heads hitting the platters and being 'sanded' right off and there isn't anything you can do about that. Other times it may just be a head is stuck and freeing it will get you some, or all, of it back depending on where it is stuck.
If you decide to open it, please have some place to copy any data you might be able to get back ready. Ie - if you have a 2tb drive that you know is almost full with your stuff then have a drive ready that has 2tb of free space.