Uhhh, yes it does work. That is the exact progression I used to beat it.
...and they are tomatoes. It isn't a tree. Look at the end of the game and see how big those trees are. The tomatoes are on a plant, not a tree.
The main thing that needs to be improved is how long it takes to quit/start a new game. Seriously, it takes way too much time to go back to the main menu after clicking quit.