Does a teleconverter change my depth of field?

Yes, but by less than you might expect. At 15 meters, a 200mm f/2.8 lens produces roughly 897mm of total depth of field; add a 1.4x teleconverter (making it a real 280mm at a real f/4, since the converter narrows the physical aperture along with extending focal length) and depth of field narrows to roughly 650mm — a real but moderate reduction, not as dramatic as the reach increase alone might suggest.

Why Two Effects Partially Cancel Each Other Out

A teleconverter multiplies real focal length, which narrows depth of field, but it also narrows the real aperture by that same factor (the physical opening diameter doesn't change, so the f-number increases proportionally with the extended focal length), which widens depth of field back somewhat. These two effects push in opposite directions, so the net change is smaller than either effect would produce alone — genuinely narrower depth of field, but a more moderate shift than the extra reach alone implies.

A 2x Converter Shows the Same Pattern, More Pronounced

A 2x teleconverter on the same 200mm f/2.8 lens (making it a real 400mm at a real f/5.6) narrows total depth of field further, to roughly 442mm at the same distance — still a real reduction, but again more moderate than doubling the focal length alone would suggest, for the identical reason: the aperture narrowing that comes with a 2x converter partially offsets the focal-length-driven narrowing.

Compare your own lens with and without a teleconverter directly in the DoF & Hyperfocal Calculator, pre-filled with a 200mm f/2.8 plus 1.4x converter.