Does an American citizen traveling from New York to Kathmandu via Delhi need to clear customs and immigration if holding a boarding pass to the final destination? Can he access the transit hotel in the airport without a visa?
If you already hold the onward boarding pass, you do not need to pass immigration as India allows Transit Without Visa. See this answer for a first hand account. Even if you need to collect luggage at DEL, there are anecdotes of airlines doing it for you (See this question).
The airport hotel is accessible to transit passengers without an Indian visa. From the website (Emphasis mine)
Valid International Airline Boarding Pass for onward journey is mandatory to access the International Wing. INDIAN VISA is not a prerequisite for passenger coming from an International Destination transiting through Delhi to next International Destination. Checked-in luggage transfer is responsibility of the respective airlines and information regarding the same can be obtained at the International Transfer Desk. Passenger can access the hotel with hand luggage after security check. The International Wing is located at on the 5th Floor accessible from the International Retail area. Transit Passengers can access our hotel after crossing the International Transfer desk followed by security check.
It also has this piece of advice for transit passengers (emphasis mine)
Passengers coming from International Destination and transit through Delhi to next International Destination are requested to book the International wing. Guests do not need an INDIAN VISA. Guests will need to have a valid boarding pass to stay at the hotel.The maximum length of stay for any guest cannot exceed 24 hours and hence the hotel would be able to provide a room only 24 hours prior to the guest's flight. Please note that once the guest checks-in to the hotel, they are not allowed to leave the hotel premises.
This info is also provided by Timatic
TWOV (Transit Without Visa):
Visa required, except for Holders of confirmed onward tickets for a max. transit time of 24 hours. - Hotel facilities are available in Terminal 3 at Delhi (DEL) if holding a boarding card for the connecting flight.