Yes and no. SDL 2.x is not backwards compatible with SDL 1.x (and that was an annoyance of mine) but at some point someone wrote an SDL 1.x implementation on top of SDL 2.x that got official blessing, so at least games using SDL 1.x can be made to use SDL 2.x "under the hood" be it in source code form or binary-only form.

Though you can't take an SDL 1.x game and convert it piecemeal to SDL 2.x as the APIs are not backwards compatible, it is an all-or-nothing change.