i wouldnt combine a co2 with an air pump. no, you dont need a co2 to grow plants. you will need adequate lighting though. about 2 watts per gallon is supposed to work wonders.
CO2 injection is optional. You're fine without it. If your tank is understocked, then no need to get an airpump. Just divert the output flow to create surface agitation. Save your money for battery-operated airpumps.
I agree with Lupin. The simple ripple from a HOB is enough surface agitation for a well stocked tank. And no need for Co2 injection, it just makes things more complicated.