Yes and no.
There are two factors that determine an object's visible size from the planet: its physical size and its orbital distance.
Physical size is essentially independent; it can be virtually anything you like. The main thing that matters in orbital dynamics is mass, and as long as it stays low compared to the planet (I've heard 1/50th or 1/100th of the planet or less) it will have negligible effect on the orbit. Depending on the body's composition and structure, it can have varying densities, so the same mass can be more or less compact as you desire. Compare for instance Mars's two moons, which are (relatively) lightweight carbonaceous asteroids, with Earth's own moon, which is composed of heavier rock and is about twice as dense.
The other factor is orbital distance, and this plays directly into the orbital period. The further out the orbiting body is, the longer it will take to complete its orbit. You can see the equations governing this behavior here, but the gist is that the satellite's orbital period is proportionate to the one-and-a-halfth power of the orbital distance. Meanwhile the apparent diameter falls off linearly with distance.