FR-4 RF attenuation (when used as an enclosure)
FR-4 is non-conductive material with a dielectric constant of 4.2 - 4.8 (varies with frequency and manufacturer) and relative permeability of 1, (see Wikipedia page for FR-4). With such characteristics, I expect it to cause reflections (far-field) and detuning of antenna (near-field). The FR-4 causes a discontinuity in the RF link, since its characteristics differ from characteristics of free space (air or vacuum).

But with a finite thickness, the effect might not be too dramatic. 2.4 GHz has a wavelength of 125 mm, which is much more than the thickness of FR-4 (I assume you would be using something like 1.6 mm thickness). But the transmission through the FR-4 is also dependent on other dimensions than the thickness (how much of the Fresnel zone the FR-4 is blocking). So, if you enclose the antenna from all sides, Fresnel zone will definitely be blocked.

Unfortunately I couldn't find any research from which you could directly interpret the effects of FR-4 to the RF link. Many antennas have a polymer cover, which is also a lossy material. Plastics seem to have a bit lower dielectric constant than FR-4, but maybe they can be the starting point for estimating the performance of FR-4.

I hope you try it, and share your research here. I'd be interested in reading the results.