Yes and no.

The initial investment would be buying spellbook ($10) which allows you to play and earn when you play the game. You can then post Splinterlands related stuff and may or may not earn some upvotes from Splinterlands. If you do, you can turn the rewards into DEC, the game currency, to fund yourself playing the game.

Then you also earn another currency called SPS from playing Splinterlands that you can turn into DEC or Hive to fund your Splinterlands account and/or Hive account and just do the cycle.

For the Land, which is a feature of Splinterlands, you need to buy a plot and invest some DEC to make it work.

So, technically, you fund initially, then let it fund itself afterwards. You can check the Splinterlands contest here: @splinterlands