That depends on your definition of "working". If it means "existing on paper and in the minds of a few delusional individuals", maybe.
To me, a "working" government in exile is recognized by at least a few real governments having real power. Say De Gaulle in London in 1940-44. While not defining itself an empire, France did have a lot of colonies, and indeed Gaullist forces (with a hefty dose of British troops) began retaking control of those first.
For how long can that last? Probably for as long as the countries recognizing the exiled government are at war with the de facto government. A cold war can also be enough, for a while. Eventually, practicality wins.