No. There were flirting between Barbara/Batgirl and Dick/Robin when they work together in Batman Family comic (Dick was a College student at that point). Tha was pre-CoIE.
In Post-CoIE, Dixon will make a retcon, so Dick/Robin as a teenager has an unrequited crush on Barbara/Batgirl (which never happened in Pre-CoIE). They only develop a real relationship when they are adults.
In Flashpoint, where Dick/Robin and Barbara/Batgirl start to fight crime as teenagers, we see they flirt in these adventures.