You kind of can. If the person opening the save has the element installed it'll automatically execute. Although that's not embedding in the slightest :P
(1) If you want to save a simulation into the online server, just click the new save button. (2) If you want to save a Lua/C++ element into the online server, that is not possible.
You have to distribute your element by other means (for example http://bpaste.net combined with a forum post), and ask people opening your simulations to have the same element installed. Saves can easily use Lua elements, even when the saves have been uploaded to the online server.