First of all, welcome to the forums! I don't feel that I am an expert at all of this, but I'll do my best to help you out!
In theory, it is totally possible to run your keyboard through a bunch of pedals and such (just like you would a guitar). However, I wouldn't recommend it. As far as the sounds that you can achieve with guitar pedals, the sky is pretty much the limit. With a lot of tweaking and experimenting you can create any sound you want (including an organ-like sound). One problem with using pedals to obtain your sound is practicality. It's not practical for a keyboardist to have a ton of pedals that he is paying attention to live, while playing all the different parts assigned to him in a song. Another problem is the fact that you really don't hear of many keyboardists using this method, which would imply that it isn't the best route to go. I do know, however, that using reverb/overdrive/delay pedals is common in the professional keyboardist world.
What I would recommend for you, b0mb, is to use a laptop with software such as Reason to create and order all of these sounds for you. I am assuming that if you are contemplating purchasing pedal(s) then you would have a budget to shop around for some good software to accomplish your goal. There are so many different software options for you. As for all of these options, pros/cons and the best what-you-get-for-your-money ratio I am not sure. Reason is what I use, along with Abelton, and they are both AMAZING. I do know that the Korg SP200 does have MIDI that opens up a lot of doors for you. I would take advantage of those doors and begin researching some audio software. Again, I do recommend Reason. It's pretty much got everything that you are looking for, need, and more than you want most likely.