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So could this (would this?) be used to simulate antenna design?

MEEP is typically used in the nanophotonics community for simulating things metamaterials, photonic crystals, and waveguides. All of which can be thought of as optical antennas.

You could use it to do that, though my non-expert understanding is that FEM will beat out FDTD for antenna design on many occasions.

It depends on the application. FEM software like COMSOL and CST Studio is typically used for simulating individual antennas. FDTD software like Lumerical is more popular for simulating metamaterials, which are basically large periodic arrays of sub-wavelength antennas.

FEM is typically frequency domain, hence it's good for structures with high Q such as cavity filters, where you know the resonance a-prior. The time domain methods are nicer for transmission lines and antennas since the whole response can be computed at once.

CST has many solvers built it, not just FEM; the time domain is the most popular.

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