That rule of thumb about needing at least a 1/4 wave radius of ground plane, is one that's used for a 1/4 wave monopole antenna.
At 2.4GHz what that would look like is a 6cm x 6cm groundplane, with a 3cm long wire element sticking vertically upwards from the middle of it.
If you can arrange that, great. It should radiate reasonably well upwards and outwards in all directions, with a null vertically upwards and little gain towards the backside of the board. More groundplane than that is fine - an ideal monopole sits on an infinite groundplane, after all. You get some variation in gain and takeoff angle depending on the groundplane size. Make the groundplane too small and the antenna will no longer resonate naturally at the operating frequency, so you'll find it harder to match to and it will have poor efficiency.
But your corner-mounted chip antenna bears very little resemblance to that configuration. Yes, there's about a 1/4 wave of electrical length in that helix, but it's not going to behave in at all the same way as a straight 1/4 wave wire element, so pretending it's a monopole isn't going to bring you to meaningful conclusions. It's going to do something weird, and your options if you want to know how it behaves in a given configuration are to either simulate it, test it, or stick to the known design the manufacturer provides. You're not going to get far with throwing rules of thumb at it from a very different, and much simpler, form of antenna.
At the end of the day, most of the time you can stick any old chip element on any old board and it will radiate to some extent. If you only need 100', outdoors, and you have a PA on there then it may well be fine. But don't expect that 3D plot in the datasheet to even vaguely resemble what the radiation pattern will look like in your own configuration.
(The colours are gain, and correspond to distance from the origin. The lines are just the polygon mesh that it's using to display the 3D shape, they don't mean anything as lines)