No, the 9.0.1 Extension Library does not work with a 9.0 client/server.
You would get runtime Errors, like this one:
java.lang.NoSuchMethodError: com/ibm/xsp/util/JSUtil.addSingleQuoteString(Ljava/lang/StringBuilder;Ljava/lang/String;)V
at com.ibm.xsp.extlib.renderkit.html_extended.layout.AbstractApplicationLayoutRenderer.writeSearchBoxAbstractApplicationLayoutRenderer.java:798)
reported here:
http://www.openntf.org/main.nsf/project.xsp?r=project/XPages%20Extension%20Library/defects/8B481EF5FF39C21286257CB5003E94D4