Does foam have the ability to broaden the bandwidth of an antenna?
The foam is there because many foams can have a very low relative permittivity (essentially \$\epsilon_R = 1\$) as they are mostly filled with air. If you look at the fundamentals of patch antennas, you can see that in general, a larger distance between patch and ground plane result in a higher bandwidth. 

One way to do this is to keep the patch further away from the ground plane with standoffs, and have air in between. The foam has similar electrical performance as air but unlike air, the foam can be used structurally as well, to keep a specific and precise distance between the patch and the feed/groundplane, and to ensure that nothing gets in between the patch and groundplane to interfere with the performance.