Regardless of whether or not transport links are improved Finningley will never benefit Sheffield to an extent greater than the fact that local residents have one more airport to go on holiday from.
It's all about facilitating commerce and taking advantage of the fact that business takes the line of least resistance. If Gamston Airport near Retford can manage to justify its existence financially then surely Sheffield City Airport could.
At certain times of the day I reckon that I could get to Leeds city centre in less time from Sheffield City Airport than I could from Leeds Bradford Airport.