No, it doesn't work to select all text from an old document and paste it, even into the new template that Yvan made me. I even tried pasting the text, then selecting all and changing the font to Baskerville. That worked fine, and the bold and italic functioned as they should, but when I selected again and tried to change the font back to Arial, it wouldn't change to Arial. It remained in Baskerville font.
Something is contained in the text from the old documents that is preventing Pages from working correctly. I'm not sure how to deal with changing all these old docs over. I guess I'll have to convert them to plain text first, to remove formatting?