Will it work? Absolutly. Will it taste like champagne? Not as positive, but it will be a "sparkling wine" without a doubt.
Most large wineries that make sparkling wines simply :
1-create the wine
2-filter it until all yeast and sediment are cleared
3-use CO2 to 'force carb' the wine to make it bubbly
Try mixing the three wines in different ratios, and testing them. Remember that the carbination will give it a bit of a 'bite'.