For a camera of that type...a 'teleconverter' is just a lens that attaches onto the front of the lens and magnifies the image.
It will degrade the image quality, no question of that. So you need to decide if it's worth the loss of image quality.
Personally, I'd just recommend that you use a tripod (or other support) and do your best to get a sharp shot without the TC...and then crop the image afterward.
Definitely try it out first, as the quality of a teleconverter is impossible to predict! as it's entirely dependent upon the lens it's matched with.
Typically, a 1.4x teleconverter is almost always a useful tool, whereas a 2x converter is only useful when it's nicely matched to a lens.
The final photo is the combination of your lens and the converter... most of the time the converter will amplify the already existing issues with your lens or introduce new problems, (softness, CA), however in rare and random circumstances I've actually encountered teleconverters that improved image quality--I'm guessing that whatever optical flaws the converter had were corrective to the flaws in my lens--like a eye-glasses.