Looking at examples which involve classical groups, I'd say offhand that the answer to your question is no.  A useful source to consult is the article on "Conjugacy classes" by Springer and Steinberg in the 1970 Lecture Notes in Mathematics No. 131 (IAS seminar write-ups), especially part IV.2 of the article.    Here they describe for classical groups explicit Levi factors in centralizers of unipotent or nilpotent elements (which are mostly interchangeable in characteristic 0).    For example, if you start with a symplectic group (simply connected), you typically get a Levi factor which is a product of various symplectic and orthogonal groups.    The latter are not simply connected, however.   
(In most of this discussion, the characteristic of the field isn't important.)