No it doesn't work. It updates Box table using a current record in the NewLocation table (w/o moving record pointer in the NewLocation table). Run your code with small modification I made to see for yourself.
The following does work

CREATE CURSOR Box (box c(10), freezer c(10))
INSERT INTO Box (box, freezer) VALUES ("1","123")
INSERT INTO Box (box, freezer) VALUES ("2","999")
INSERT INTO Box (box, freezer) VALUES ("3","999")

CREATE CURSOR NewLocation (box c(10), freezer c(10))
INSERT INTO NewLocation (box, freezer) VALUES ("2","222")
INSERT INTO NewLocation (box, freezer) VALUES ("3","333")
INSERT INTO NewLocation (box, freezer) VALUES ("1","111")
INDEX ON box TAG box

SELECT Box
UPDATE Box SET freezer = NewLocation.freezer WHERE SEEK(Box,  "NewLocation", "box")

In VFP9

UPDATE Box SET freezer = NewLocation.freezer ;
	FROM Box ;
	JOIN NewLocation ON Box.Box = NewLocation.Box

>Here you have an example (partial) that is working

>CREATE CURSOR Box (box c(10), freezer c(10))
>INSERT INTO Box (box, freezer) VALUES ("1","123")
>INSERT INTO Box (box, freezer) VALUES ("2","999")
>INSERT INTO Box (box, freezer) VALUES ("3","999")
>CREATE CURSOR NewLocation (box c(10), freezer c(10))
>INSERT INTO NewLocation (box, freezer) VALUES ("2","123")
***
SKIP
***
>SELECT Box
>UPDATE Box SET freezer = NewLocation.freezer WHERE Box = NewLocation.box