After a brief period (you will not be able to prevent GC as citizens of the EU from freely moving around in the break away state, voting, becoming candidates in elections and generally enjoying basic democratic EU freedoms:
Article 8a
Every citizen of the Union shall have the right to reside and move freely within the territory of the Member States, subject to the limitations and conditions laid down in this treaty and by the measures adopted to give it effect.
The council may adopt provisions with a view to facilitating the rights referred to in paragraph 1; save as otherwise provided in this Treaty, the Council shall act unanimously on a proposal from the Commission after obtaining the assent of the European Parliament.
Article 8b
Every citizen of the Union residing in a Member State of which he is not a national shall have the right to vote and stand as a candidate in municipal elections in the member state in which he resides, under the same conditions as nationals of that State. This right shall be exercised subject to detailed arrangements to be adopted before 31 December 1994 by the Council, acting unanimously on a proposal from the Commission and after consulting the European Parliament; these arrangements may provide for derogation's where warranted by problems specific to a member state.
Without prejudice to Article 1 38(3) and to the provisions adopted for its implementation, every citizen of the Union residing in a Member State of which he is not a national shall have the right to vote and stand as a candidate in elections to the European Parliament in the member state in which he resides, under the same conditions as nationals of that State. This right shall be exercised subject to detailed arrangements to be adopted before 31 December 1993 by the Council, acting unanimously on a proposal from the Commission and after consulting the European Parliament; these arrangements may provide for derogation's where warranted by problems specific to a member state.
I mean, then your "political equality" and whatever else could not be indefinitely guaranteed.