Hi Leo,
Yes, you can exchange the pass at Narita for use the same day and use on the Hikari bullet the following day. About which option is better for you, a 7 day rail pass will be worthwhile if you spend oer ¥28,300 on JR tickets so lets take a look at your projected costs:
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Narita airport terminal 1 > Tokyo: ¥3140, (62mins, 79km)
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Tokyo > Nagoya: ¥10780, (126mins, 366km)
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Nagoya > Tokyo: ¥10780, (106mins, 366km)
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Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
TOTAL: ¥27840 for 4 legs
As you can see there's really not much in it. Individual tickets come in at ¥460 cheaper, but you can easily make this up through using JR trains around Tokyo or by doing any further JR travel (which the JR Pass give you flexibility to do).
Your choice of JR Pass vs JR tickets rests on whether you think you'll do any further travel than the itinerary you list, or would like the flexibility to change your plans while you are in Tokyo (for example through a day trip to Nikko).
Hope this helps!