Can I board a Sri Lankan train without a reserved seat?

Yes. Anyone can get into the unreserved second- or third-class carriages by buying a normal ticket at the station right before the train leaves.

This can be handy if you decide late. Still, there is a catch. If the train is very busy, you may end up standing for a long time. If you want a chance to sit, go to the platform early. Then wait near the spot where the doors will open.