Does different Base Year in Price Index affected conversion of nominal value to the real value?
This question might be better suited for a statistics group, but if I understand you correctly you're going to compare two prices from different price indeces and see if there's a difference in the growth? There's really nothing wrong with the reasoning, but you should take the results you get with a grain of salt as you'll be comparing two indeces with different samples.

The different base year is not a problem as long as the variables you're dividing are from the same dataset. When price indices are renewed, the sample is often changed, so this is why you should be aware what you're doing when comparing between different base years.