Yes, as long as you can provide episode download data via screenshots, that will suffice for most sponsors.
If your current podcast hosting platform or setup does not provide any analytics for your podcast, we'd recommend moving your show to a hosting platform that does. You can see a list of Apple's recommended podcast hosting platforms here.
We have also developed a new feature that allows for manual stats upload. Select manage your podcast in your settings, and then click on the upload stats tab.