Advertising sales is a good indicator as to how well the economy is doing - if times are good then people advertise, if everyone is screaming recession then there is not so much money around to advertise. Hence, if Google does well does that mean the economy as a whole is doing well? Is the Google share price a good indicator, perhaps a better indicator than conventional metrics such as employment level or the FTSE?
No, GDP growth and unemployment are better measures.
GDP alone is a sufficient statistic, since the definition of a recession is very precise, and is based on GDP growth.