Yes, this is how the benchmark is calculated.
I think there’s another way to get the info you’re looking for: you can use TWR to compare with the benchmark. This will tell you if the MIX (so your strategy) is better/worse.
MWR on the other hand, tells you the impact of your timing and fees vs the index.
I was thinking about doing it the way you described and arrived at the answer that TWR is better for this, and I didn’t find other apps using MWR in this way, so that could be misleading.
Check out my article on calculating returns, but I’m happy to discuss this further 
Btw, in the future, I want to add Strategies, which will be designed to answer this question more thoroughly.