yes it does. It will not shorten the life. Its a misconception that everyone seems to believe is real. I run a 36w starter on a 15w tube... well actually two 36w starters on 2 15w tubes.
Think of it this way, most computer power supplies are rated at about 30% more wattage than is actually in use. If it was to output its total capacity, then they'd be a lot of blown up computers. A 15w bulb will only draw 15w of the 36w the unit has to offer. The actual starter bit (which glows when starting up the unit) is the only bit you need to make sure will start a 15W bulb.
Try it out, you can buy a power adapter that you plug any 230 mains supply into it and it will tell you how many watts it'll output. My tank is just over 90watts with everything on. My laptop is only 18 watts when playing call of duty and my desktop pc is 230watts on idle and 390 on load.... makes you wander how much electricity a desktop pc wastes.