I think it will work, but if it doesn't, strongly consider applying Sheldon Brown's technique of using the narrower 9-speed spacers to build an 8-speed that is only marginally wider than a 7-speed, which the NR handles easily. (I have a 7-speed SRAM freewheel and a 1980 NR rear derailleur on my Bianchi.)
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069