I've used this a couple of times. The baggage delivery service is quite popular with Japanese, especially if you consider the fact that most people would have to drag the bag 10-15 minutes to the closest train station (unless they shell out money for a taxi), then wrestle it on the escalator if they're lucky (few stations have elevators), and then find enough space on the train for the bag and themselves. The luckier people can drag the bag/take a taxi to the closest airport bus stop.

The two most popular services are run by Sagawa and Yamato Kuroneko. For Narita to a Tokyo hotel, it will be about 2000-3000 yen. Yamato Kuroneko's prices can be found here. Sagawa's prices are here (baggage delivery is done using the Hikyaku Express service). Location for the drop-off points can be found here.

Whether it makes sense for your wife to just haul the bag(s) with her onto the train/bus or use this service depends on a number of factors. It includes how many, how big, and how heavy are the bags; which hotel she's staying at; and how willing she is to drag the bags along vs. taking the (very small) risk that the delivery service will damage/lose her baggage.

For example, if I'm carrying a 28 inch bag that weighs 30 pounds plus my golf clubs, I would start thinking about baggage delivery unless I was staying at say, the Hyatt Regency in Shinjuku, in which case I would just drag all my bags to the airport bus since it stops in front of the hotel.

BTW, the trains are never crowded leaving the airport. It's the trains that you have to transfer to inside of Tokyo in order to get to your hotel that are crowded, especially during rush hour. Plus, it's a pain hauling your bags up and down platforms and halls to get to the escalator/elevator.