Based on the premise set in the pilot, I will say No. As it looks fully self-contained.
It's a show about an odd-one-out kid which is apparently Sheldon, that's it. We get to know about his family dynamics when he was young. Though I have not seen The Big Bang Theory much, still I was fully able to understand it. It even gave no vibe of The Big Bang Theory to me and appear like a different show altogether.
And from the old cast, we just hear Jim Parsons doing voice over and Zoe Perry reprising her mother's younger version, which is played by her mother Laurie Metcalf in TBBT. And there is a possibility that we will be getting the answer of Sheldon's personality trait from the new show as we got about his inability of driving.