This is definitely possible - you'll create an image file with no text in it, in some format Imagemagick understands (i.e., not PSD - JPEG or PNG are two common formats), and then draw some text on top of it. The same technique is used to produce those captcha images.
You can find a really basic tutorial showing how this might work here.
Obviously you can do much more complex things than that page is showing, but it should get you started. The full PHP ImageMagick API is very well documented in the main PHP documentation, which can be found here.