First off, the TC unit MUST actually physically mate with any lens it is to be used with: many TC units have a forward-projecting element that sticks out from the TC unit's mounting flange, which means that "some" lenses will not even mount onto some TC units. So, there is that caution. OTHER TC units, such as some made by Kenko for example, have a fairly deeply-recessed front element on the teleconerter, and so those will allow mounting many types of lenses.
I've shot a few 50mm lenses with 2x TC units of various manufacturer and various vintages; the typical result is that wide-open the image quality has some veiling glare, which is a lowered contrast, and lowered resolution. Veiling glare is an actual term, an old term; MOST 50mm primes suffer from veiling glare when shot wide-open, and adding a TC will often tremendously add to this defect--almost to the point that the shot looks like it was made with say, the Lensbaby 2.0 effects lens.
Stopped down one stop, the image quality in terms of overall sharpness and contrast will usually be noticeably better--but NOT "great". Closed down another stop, or another two stops, image quality will probably be adequate for many uses. Adding the cheapest, crummiest 2x converter to a 50mm lens can give you a sort of dreamy look, which you might like for portraits; a really cruddy 2x + a-not-well-matched-to-that-converter lens lash-up it will often result in what looks sort of like adding negative clarity in Lightroom.
Be aware also that adding a 2x TC will usually affect the focusing performance of the lens. The best thing to do is to TRY IT and see how it works, for you, with whatever lens and whatever TC unit you have available to you; some of the old, manual focus, used $8 to $15 no-name TC units might be rubbish, but say, a high-grade, 7-element TC unit might be much better. I have a $19 Tokina 2x and a $299 Nikon 2x...one is very yucky...the other is much better in quality.