Not in my experience, I swear by the stuff, second stage labour for me was 26 mins however it took me 40 mins to push placenta out even with the injection. The MW this time told me that it can be common for it to take a little longer for your placenta to come out if the rest of your labour was quite quick (mine was 4 hours up to birth). So yeah I love RLT and credit it with a quick second stage for me and I also got god awful after pains which can be credited to RLT (a good thing for snapping you back down to size quickly, I was in my pre pregnancy jeans the next day) but for me I don't think it affected third stage, well unless it was meant to be longer than 40 mins in which case I will never know lol.