I think that you want a longer focal length, so that the 200mm becomes 300 or 400mm? Most of the teleconverters are designed to work with fast (F4 or faster) primes. Pairing them with consumer zooms is not very satisfactory. A teleconverter on a consumer grade lens will work but
. The IQ will be quite bad, and with a cheap teleconverter, horrible.
. You will loose AF on most consumer zoom lenses due to high minimum aperture, even if the TC has contacts. A cheap one may not have contacts, so no AF.
. An external add on lens will have the same problems as a TC, but if it does not work, you will loose less.
The only method that I know of getting higher magnification of distant objects with decent IQ, is to get a lens that has a higher focal length. Among the lower cost zooms is the 70-300, followed by the new 200-500. Beyond that are professional zooms and telephoto primes. Ultimately if you want good good IQ, you will have to pay more.