I do not believe there is anything that for sure reveals that WFS server is GeoServer but with standard settings the schema location refers somehow to geoserver and some supported functions are special for GeoServer. However, others can implement functions using same names:
http://localhost:8080/geoserver/topp/ows?service=WFS&version=1.1.0&request=GetCapabilities
<wfs:WFS_Capabilities version="1.1.0" xsi:schemaLocation="http://www.opengis.net/wfs http://localhost:8080/geoserver/schemas/wfs/1.1.0/wfs.xsd" updateSequence="96">
<ogc:FunctionName nArgs="-6">BarnesSurface</ogc:FunctionName>
For testing is CQL_FILTER is supported you can try the "IN" filter as in http://docs.geoserver.org/stable/en/user/tutorials/cql/cql_tutorial.html
The following request will return one feature from GeoServer and probably all features from other servers (or an error). You must edit "states.1" to suit with the name of the featuretype:
http://localhost:8080/geoserver/ows?service=wfs&version=1.1.0&request=GetFeature&typename=topp:states&CQL_FILTER=IN ('states.1')