Like many questions, the general answer is "it depends".
If you're applying to programs in big cities, it's unlikely to matter. You'll match into one program, and your partner into another. Perhaps you'll match at the same program. But regardless, you'll both have lots of options and lots of combinations. The PD might contact the other program just to see how competitive your partner is, but even if they didn't apply, they'll know there are many other programs in the city that they could have applied to.
If you're applying to "stand alone" programs -- ones that have only a single institution in the area -- then it might matter. The University of Iowa in Iowa City, or University of Vermont, for example. If you couples match into programs like this, then there's only two options -- you both get spots, or neither. In that case, the two programs might review couples before offering interviews to avoid the situation where one person gets invited and the other doesn't. Or, they will all act independently and just let you sort it out.
Bottom line: it's unlikely to make any difference.