Can a specialized template method bypass the default one that would not compile due to the creation of an abstract object?

Question

It might be a weird question, but it could be quite handy in my use case.

I have the generic class:

template <typename CGtObj>
class CGtObjectsMap
{
    virtual CGtObj* newGtObject(GtId idXML, const CSAXElement *) const { return new CGtObj(idXML); } //!< can be overwritten by MyAbstractClass ;)
    virtual void loadFromXml(CSAXElement const* element);
};

with a "quite complex" loadFromXml(CSAXElement const* element) that has at one point:

template <typename CGtObj>
void CGtObjectsMap<CGtObj>::loadFromXml(const CSAXElement *element)
{
    ...
    objPtr = newGtObject(idXML, element);//new CGtObj(idXML);
    ...
}

A certain class I need to use in that CGtObjectsMap is abstract. That is why I've created the virtual method newGtObject, hoping I could avoid duplicating the whole code of loadFromXml() in a specialization of that class.

But it doesn't compile, and I'm having an error on the template standard definition of newGtObject():

error: invalid new-expression of abstract class type ‘MyAbstractClass’

coming from:

virtual CGtObj* newGtObject(GtId idXML, const CSAXElement *) const { return new CGtObj(idXML); } //!< can be overwritten by MyAbstractClass ;)

although I've specialized it:

template<>
MyAbstractClass *CGtObjectsMap<MyAbstractClass>::newGtObject(GtId idXML, const CSAXElement *element) const
{
    MyAbstractClassType type = static_cast<MyAbstractClassType>(element->childValueByName(XML_TYPE).toInt());
    return MyAbstractClass::createAction(type, idXML);
}

Is there a way to avoid that compilation issue?

(The specialization is in another file)