We were on the VFR tour in May. My photos from the illumination in St. Mark's are time-stamped right about 11:30 a.m. (yes, we were told we could take photos). So making the 11:30 Secret tour might be tight or impossible to begin with.
Be aware, also, that the RS tour itinerary is totally subject to change by your guide. We had several deviations from the "final" itinerary provided before the tour. The day we toured St. Mark's, for example, we then took a boat to Burano, so it really would not have been possible to do something on our own without skipping tour activities. Later, in Rome, our guide took us to the Vatican/Sistine Chapel in the afternoon and evening rather than morning as "scheduled." That change made it impossible for us to visit the Borghese Gallery, for which we'd already purchased tickets. Next time we take an RS tour, we'll likely avoid making set-in-stone plans for our free time and just try to go with the flow of whatever presents itself.
All that said, we did the Secret tour on our own the day before our VFR tour began, and it was fine. If you do manage to fit it in somewhere, be aware that you're free to explore the Doge's Palace after the tour, so you don't need to buy a separate ticket for that. Good luck with your planning.