It depends what you mean by "influenced by"

I came upon this just now in Google Search:

They are right, of course. The one they call "Real GDP" changes because of changes in the output we produce, but not because of changes in prices. The one they call "Nominal GDP" changes because of changes in output and because of changes in prices. 

If we say Nominal GDP is all of the output purchased in a year, measured at that year's prices, then Nominal GDP is a measure of actual spending. If we say Real GDP is all of the output purchased in a year, measured at 2012 prices, then Real GDP is a measure of what that spending would have been if prices never went up. Actual things are called "nominal", and fantasies are called "real". This, it seems, is the way economists think. That being the case, it must be easy for them to say Real GDP is "not influenced by changes in prices."

As for myself, I understand that raising interest rates slows the economy and reduces inflation. I understand this is the preferred economic policy of many nations. I do not think it is the best way to reduce inflation, nor even a very good way, but that is not my topic here. So I say, without complaining, that raising interest rates slows the economy and reduces inflation.

Now, Nominal GDP measures changing output at changing prices. And Real GDP measures changing output at unchanging prices. But to get prices to be really "unchanging" we would have to reduce inflation. 

And reducing inflation slows the economy.

And "slowing the economy" means reducing the amount of output we produce. So, if the question is Do changing prices influence Real GDP? then the answer is Yes, absolutely, they do.

To expand on that thought: If by "price changes" we mean either "prices going up because of inflation" or "policies that reduce inflation", again I have to say yes, such changes in the price level do influence Real GDP growth. Yes, absolutely.

That's my short answer.