G'day Oldtora,
No airline pilot would ever deliberately fly into a thunderstorm, never. However if you are crossing an extensive multi-cell convective system (MCS) the limitations of the weather radar becomes apparent. While an isolated storm cell or bunch of cells will show up on the display clearly, in a extensive MCS the radar would be pretty much saturated, not with water but with radar returns, and it would be very difficult to determine where the individual cells and so the worst turbulence actually was. Another problem is that one cell can be hidden by another, just like having something in the way of the radar beam, and you might manouvre to avoid one cell and unwittingly find yourself flying straight into another one with little or no chance of avoiding it.
I hope this is the information you want.
Regards,
BH.