Do you use more mobile data with Wi-Fi off than with Wi-Fi on (connected to Wi-Fi or not) Does using your mobile data while having Wi-Fi off when not connected burn data faster than using mobile data while having Wi-Fi on when not connected to Wi-Fi?
You can measure this yourself by going to settings app and using the reset option to then track data and watch how much you use over a set period and then again repeating the steps with Wi-Fi in the other state.

In general, you should leave Wi-Fi on so that it connects when it can if you are concerned with mobile data usage.

I can't see a situation where an app developer would notice that Wi-Fi was off and then send more data over mobile/cellular data, but it's something that a developer could in fact do.

You'd have to measure things to be 100% sure. My guess is even if there is a difference, it would be so small as to not matter, though.