Depends on what you mean 'dominant'.
In terms of population, no, it would be one of the most populous, but barring some horrible event(s) the Indian subcontinent and East Asia would beat it out.
In terms of economics it's possible, it does afterall sit at the crossroads of very important trade-routes and has a great deal of economic potential itself.
In terms of politics it's possible, especially if it makes sustained contacts and trade with other parts of the world and becomes a colonial power itself.