While I can't speak for this specific half marathon, we were at Epcot for the full marathon a few years ago and we first went to Animal Kingdom (just my husband and I) while my son and his family went to Magic Kingdom. Then we went to Epcot while the full marathon was in the parks (I honestly don't know where it ended up). What we found was things were just as normal as they could be with lots of Cast Members directing foot traffic so the runners were not distracted by anything. And after the runners were done, Epcot seemed the same as normal.
Quite honestly, if in any crowded conditions, Epcot is our favorite place to be because there are so many places to just take a break. For example, the Friday after Thanksgiving, it was a bit more crowded but we found an off the beaten path place to actually sit and be able to watch the first night of the holiday tag of Illuminations.
But consider what your wife will want/need to do after the marathon. You might have to leave Epcot for her to get a breather or changed or whatever. You might not know that until after the race.