How side-by-side are we talking? If the antennas are closer than their size, yeah, it won’t necessarily work the same way because they’ll act like one antenna. If they’re too far apart for “near field” effects (or if your antenna was tiny relative to the wave to start with, like with AM radio) it won’t matter, because the wave in question will just kind of ooze around any obstruction, and received power will just go with inverse square of distance to source again.

In practice, it’s unlikely to matter so much how loud the signal is, because (unless you’re using a crystal radio) you are definitely going to amplify it quite a lot before it’s useful, anyway. More of concern is how loud it is relative to any random noise that’s present, which is not so dependent on antenna area.

Edit: I suppose if it’s between you and the source, it will dim the signal a tiny, tiny little bit. Not the way a bigger thing can cast a shadow, though; think more like a slightly dirty lens.