Devocole,
I got a little confused about "venturi" also when I got into this hobby and built my external DIY reactor, so I hear you. Although there are 2 possible locations with this design to put your venturi loops in the reactor, you only use one of them. I believe that most people just use the one on the side and use the top tube as a bleeder valve to allow the bleeding off of air/CO2 collected at the top of the reactor.
Personally, I did not like the side tube and put 2 venturi tubes in the top ... one to feed the accumulated CO2 back into the pump and one to bleed with, which allows my reactor to fill completely with water very quickly.
Very simply, here is what your venturi loop will do for you: As CO2 dissolution slows down after a while, CO2 will often accumulate at the top of the reactor. When the level of CO2 accumulates to the level of your venturi loop, the venturi kicks in. The suction from the pump ("venturi") pulls the CO2 in and the pump impeller chops the CO2 into very small bubbles. The little bubbles do not rise like big bubbles in the reactor, they flow thru with the water and come out of your output nozzle as a fine mist.
This reactor surely would work with an inline pump as you are asking. Many folks simply put it inline with one of their canister filter's lines -- the output, I believe. You can still do the venturi loop with this method. If you decide to try the inline method, many here will be able to give you some good advice.