Come across this video: http://www.youtube.com/watch?v=bggUviXnIqw

How do you think, is it possible to use one and the same motor as starter and generator?

I had a mid 70's Yamaha RD200 2-stroke twin that used the generator for both charging and starting. This was a generator with brushes, not an alternator.  

I don't think an alternator could be used as a starter. I assume it would require an AC voltage source to run as a motor. Brushless AC motors do not have much startup torque.  That is why all the big AC motors around your house use capacitors to help them spin up from a stop.

I had a Suzuki LJ20 2 stroke 4x4 that used the generator as the starter, too.
Back to the OP, it would surely be more trouble than it's worth to get a brushless outrunner to work like you want. That said, the ones used on E bicycles can make a ton of power and support dynamic braking so who knows?....

You might be able to replace the flywheel with a large diameter, low KV brushless  that turns at engine speed, perhaps. If you wanted to replace the starter motor with a brushless and use it to generate, you'd have to ballrace the intermediate gear, and even then the starter would be spinning at insane revs once the engine is running. Too much wear and tear IMO.

The first electric starter for a car was invented by Charles Ketteing amd used on a car in 1913.  He started the Dayton Electric Company (DELCO)used in 1913.  Soon after that they experimented with starter/generators with brushes and they devices were huge and weighed about 50 pounds.  Soon thereafter they learned that the starter and genertor could be more reliable, more efficient and smaller if they were seperate.  It took a long time, but eventually the generator was replaced with an alternator which is more efficient, smaller and lighter than the generator.

I am not sure what you are trying to accomplish here. Changing to an charging/starting system will most likely not be more reliable than what you alreay have, and you will never recoup the time and money it takes to design and build something for the Savage.  Your Savage already has a brushless alternator.  The starter has brushes - and it works just fine when you need it and it will outlast your engne as long as you don't overheat it by cranking too long on an engine that won't start.  There was one member that cranked so long the glue that holds the magnets in place melted, and they came loose and locked up the starter.

The RD200 Yamaha was a small 200cc twin 2 stroke and the power needed to turn that engine over is considerably less than the 650cc Savage 4 stroke.  Yamaha experimented with the system and for a while  and they had an electric start 175 enduro that used the same type system and the left side engine case had a large round bump where the rotor and stator lived....not really ideal for an off road bike to be overly wide a the engine case.  I can't help but think that Yamaha abandoned this system when it proved not to be any better than the alternator and seperate starter system.

If you watch the YouTube video closely, you can see that even with that large ring gear and low compression 5hp lawn mower engine - several times the stator fails to have enough strength to push the engine over top dead center.  It would not have a chance on the Savage motor.