Is it important to file a new soldering iron tip before tinning?

Never file a soldering tip. Filing it will remove the protective layer, allowing the metal underneath to be eaten away by solder resulting in permanent damage over time. Tin it immediately once it first starts heating up, and every few times you use it as required.

No.

The best way to keep a soldering iron tip in good shape is by using "tip tinner" - available at the usual places.

It is well worth the modest investment, regardless of the cost of the iron itself.

Bottom line is that you want it to actually work. That stuff is great.

Whenever I turn on my iron and it heats up I push the tip it into this powder, (where it melts to it), wipe it on a damp sponge, then apply a bit of solder. Then when I am finished working, I wipe it off again, shut off the power and push it into this powder again so it cools all nice and clean.

As said by Ignacio ....for most modern hobby tips (certainly for PCB/electronic work) you would never file them. The surface is plated to prevent the copper heat conductor from dissolving in the solder.

Read this for help on the modern plated tip.

That said, there are still plain copper tips produced (typically very large as used in stained glass hobby work) that do need filed. The copper dissolves in the solder as it's used so you end up with work pits in it.