Could Battenberg take a postwar imperial role?

Could Battenberg have taken a postwar role similar to Jellicoe's mission in Australia?

Yes, a similar appointment is possible, although the family obligations, financial losses, and early death of his historical retirement would limit it if repeated.

Battenberg spent much of the historical postwar period recovering relatives and arranging the burial of Grand Duchess Elizabeth in Jerusalem. Russian investments were seized, while the collapse of the German mark destroyed the value of his German property. Those losses added to the financial pressure associated with giving up Kent House. In August 1921 he became Admiral of the Fleet on the retired list, and he died that September of heart failure following influenza. These events would leave little time for an imperial appointment if his family circumstances and health followed the same course in the altered war.