No. That would be a very bad idea. In order for global currency to be viable, several conditions must be in place, including common response to external shocks, free trade, unrestricted mobility of capital and labor, and a common tax and transfer system.
Just one example. Say, the oil prices are going up, just as they are now. As a result, Norway, a major oil exporter, experiences an economic boom, so Norway's central bank is running a monetary contraction. At the same time, Japan, a major oil importer, experiences and economic slump, so Japan's central bank is running a monetary expansion. If Japan and Norway had a common currency, this would be impossible; both countries would have to have the same monetary policy, so either Norway would have high inflation or Japan would have a recession...
Interestingly, the answer to this question has been known since 1960s. See, for example:
Mundell, R.A. (1961), "A Theory of Optimum Currency Areas", American Economic Review 51: 657-665.
McKinnon, R.I. (1963), "Optimum Currency Areas", American Economic Review 53, 717-724.
Kenen, P. B. (1969), "The Theory of Optimum Currency Areas: An Eclectic View", in Mundell, R.A. and Swoboda, A.K. (eds.), Monetary Problems of the International Economy (Chicago: University of Chicago Press).