Can tricolour LEDs be connected in series?
The LED described would these days more commonly be called a bi-color LED (the term tri-color refers to LED assemblies with red, green, and blue diodes); it does not allow for series connection since the two diodes are wired cathode-to-cathode.  Some other bicolor diodes are wired anode-to-cathode, thus allowing series or reverse-parallel operation, but the one you linked isn't one of them.