Yes, but if you donnot need to invest into science, then you have little scarcity of gold unless you have a really large army. In the later case market places pay of both because of happiness and also simply for unit support.Hmm....why do you say so? Gold is important for supporting big armies and luxuries for happiness.
Without accelerated production 2 workers per city is usually reasonably so that workers can keep up with a decent growth rate.Why 3+ per city and not 2 for example? What are the specifics of the scenario that lead you to this conclusion?
With accelerated production you grow twice as fast, hence you need twice as many workers. Of course you soon reach a point when almost all relevant tiles are improved and workers can join your cities. Then your economy is turbocharged and some turns after that you are in a position to go on the offensive.