Is it appropriate to change the base year of the real GDP to a more recent one?
Changing the base year of a time series is fine if you know what you're doing, check, for example the question: How do I change the base year of real GDP using the GDP deflator and nominal GDP? 

I'd, personally, use the real GDP series - you won't gain anything substantial with the mathematical conversion. It might be an useful exercise if you, for example, were to compare GDP growth in two different countries and would like the base year to be the same.