Can I wire up a 353W projector with a 25W track light?
Ok, with the updated question... no, you really shouldn't ever power a permanently mounted light fixture from an extension cord inside a dwelling. It's acceptable in a utility outbuilding or agricultural building, but not inside a dwelling - there's too much inherent risk of an occupant (might not be you) damaging the extension cord and starting a house fire, resulting in the loss of many lives.

Your best bet would be to run a short section of WireMold (or similar brand) surface-mount conduit from an outlet box to a box on the ceiling, and hardwire the tracklights from that ceiling box.