This worked: Enter text into one cell, select the cell, copy it (cmd-c), select a range of cells, and paste. That pasted the original text into all the selected cells, even if the original cell was included.
Note that this did NOT work with selecting the text within the first cell. Pasting it over a range of cells ended up with bits of the text divided among the cells.
Trying this, the problem I see is getting the table to match the size of the labels and align with them on the page. Looking up Avery 5260 labels in Word, the labels are 1" high by 2.63" wide (though I believe that's the printable width, and the actual labels are 2.75" wide). Also, the margins at top and bottom are the same, so it doesn't matter which way you put the sheet in the printer. I didn't see any clear way to do that with Pages tables. I also couldn't find any templates for labels.