There are plenty of fat rich plants already in our world, with the only difference that those fats are stored in the fruits/seeds: avocados, olives, almonds, walnuts and all the seeds we use for extracting oil. Those plants are present in almost any climate: from the tropical regions for the avocado to colder climates for seeds like sunflower and rape.
TheHowever the fact that all the fats are addressed to the seeds and not to the mother plants seems suggesting that those are less effective in boosting growth in an already developed organism. All the bulb based plants I am aware of store energy as carbohydrates in their bulbs/roots.
It can simply be that the additional cost for building fats from sunlight and CO2 is not justified in terms of marginal gain except that for reproductive sake.