No, you will not be able to use some important dialog boxes with such a small screen. For example, the bottom of the Interpret Footage dialog box will be cut off, so you can't open the options dialog box for various footage types. That's just one example.
Thanks for the speedy reply. I have an Apple Cinema display I'll bring into work tomorrow. That has enough pixels. I don't know how to phrase this, but the machine itself doesn't have a high enough resolution, but the cinema display will. However, is After Effects dependent on the machine itself or just the monitor?
Even the most wimpy modern GPU will be able to display 1920 X 1080 which is sufficient. If your machine will drive the Cinema display then it should work.