Can an OpenGL ES fragment shader change the depth value of a fragment?

No -- gl_FragDepth (which is part of the desktop version of GLSL) is not present in OpenGL ES.

You can, however, check for the existence of GL_EXT_frag_depth. If it's available, then you can write the depth to gl_FragDepthEXT.

The extension paper gives more details about how to enable the extension and such.