Yes, but not with BorderLayout alone. The trick is to use nested JPanels,
each with its own different layout manager.
A good tutorial describing this technic is
 "Effective Layout Management: Short Course"
 http://java.sun.com/developer/onlineTraining/GUI/AWTLayoutMgr/shortcourse.html
With proper use of layout managers you should never need to call
setMaximumSize/setMinimumSize/setPreferredSize

import java.awt.BorderLayout;

import javax.swing.Box;
import javax.swing.BoxLayout;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JTextField;
import javax.swing.SwingUtilities;

public class TestBorder extends JPanel {

    TestBorder() {
        setLayout(new BorderLayout());
        add(new JTextField(), BorderLayout.PAGE_START);
        //add(new JButton("OK"), BorderLayout.LINE_END);
        JPanel p = new JPanel();
        p.setLayout(new BoxLayout(p, BoxLayout.PAGE_AXIS));
        p.add(Box.createVerticalGlue());
        p.add(new JButton("OK"));
        add(p, BorderLayout.LINE_END);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                JFrame f = new JFrame("Test BorderLayout");
                f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                f.add(new TestBorder());
                f.pack();
                f.setVisible(true);
            }
        });
    }

}

Some styles guides recommend to have a minimum size per button,
to ensure that users can click easily on it even if it has a
short label, for example "OK". To make it more difficult, some
platforms recommend that this minimum size changes with the font,
font size and resolution (dpi). For example on Windows a command
button should have a minimum width of 50 Dialog Units. Also,
different platforms use different button orders, for example
"OK, Cancel on Windows is "Cancel, OK" on the Mac.

I provide a free layout library that addresses all these issues
and that comes with a ButtonBarBuilder that will automatically
use the correct minimum sizes and gaps on Windows and Mac. See
http://forms.dev.java.net

The JGoodies Forms Demo is available here:
http://www.jgoodies.com/downloads/index.html

-Karsten