If I pay all my overdue child support on the day of sentencing, will I go to jail still?

Almost certainly yes. Sentencing is after the verdict has been reached, if you had been able to pay during court proceedings then you might have been able to mitigate the terms and type of sentence. As it stands you might still be able to make a sentence mitigation plea but it is unlikely to change the judges sentence as the case has been closed against you. HOWEVER... you should certainly tell this to your solicitor/lawyer and see what he or she says, I am not an expert but simply saying what I know based on knowledge of the UK judicial system.