Exactly, their intended duty cycle is probably something like a maximum of 1 minute powered for every 10 mins unpowered to allow for cooling. This is because starter motors aren't designed to be very efficient and to run cool but for maximum power over a short period and with minimum weight/space occupied. Having seen the 2006 Presteigne bike rally entry with a starter motor, although it looked 'fun' it wasn't to be taken seriously and when it failed part way into it, I wasn't surprised.
I'm sure bicycle chain will take the torque ok, no problem there.
Although it wouldn't snap from the power/load it's duty life will be reduced, especially if the gears aren't built into the hub. In the case of hub gears though, longevity there may then become an issue. The small gears often made from nylon aren't designed for that sort of power over any length of time. I'm not sure if other components in the drive train would last either, I believe the Presteigne entry died from broken spokes due to the extra loads.
The OP is better off with a motor designed for an electric bike or at least continuous service through a controller. Although other designs such as that intended may be able to be cobbled together to work, it'd be unlikely to last or give decent battery consumption/range. Sorry to be a dampener on things but it's best to spend money wisely in the long run.