Today, in our Shul (in Shaharit) a man walked in a little late and I guess he didn't have enough time to catch up to our Minyan. After Tefila, he asked the Gabbai if he could say his own Shemona Esre, with the first three Berachot out loud, so he could make his own Kedusha. The Gabbai agreed. After this was over, one of the congregants came to the Gabbai and told him that he probably shouldn't have let the man recite the Hazarat HaShatz. I came over to the congregant and told him that I've asked one of my Rabbanim and he said there are Posekim to rely on to do this "mini Chazara" even without people reciting Tefila with him. The congregant than tells me "what's Hacham Ovadia's opinion on this matter?" I told him I wasn't sure and that I'll look into it. This morning I contacted four Rabbanim (one of them is for Halacha LeMaaseh, the rest just because I'm interested to know their opinion) about this question and I awaiting a resonpse.
What do you think would be the Halacha based off the Poskim?