The method in the link provided by @TracyRotton seems not to be working since Jetpack 2.0 and WordPress 3.4.2.
Even replicating all database fields, it doesn't act as connected.

As the OP question is about syncing a development and a production environments, maybe it is not possible.
I haven't tested in-depth which modules work and which not, but Jetpack can be tricked into believing it is connected making the following modification in the file /plugins/jetpack/jetpack.php
.
Inside the class Jetpack_Data
, modify the very first function get_access_token
like:
class Jetpack_Data {
function get_access_token( $user_id = false ) {
return 'USER_TOKENS-VALUE-FOUND-INSIDE-THE-OPTION-JETPACK_OPTIONS'; // <---trick
if ( $user_id ) {
if ( !$tokens = Jetpack::get_option( 'user_tokens' ) ) {
return false;
}
Or simply put a return true;
instead of the user_tokens
that we can copy from inside the option jetpack_options
.
PS: the first version of this answer used another trick. Here, it is a one-line modification that catches all, in theory...