Would it be possible to have a closed loop ventilation system?

No, a fan venting into the space it's drawing from does nothing. All you are doing is moving the air in a circle. It does not create negative pressure. To generate negative pressure you have to remove air from the tent and put it somewhere else. I have done it with good success. I use a AC Infinity fan that has a programmable controller and a charcoal filter. I have it set so it only came on at lower power for very short periods. Then I had a small heater and dehumidifier inside the tent. When everything is adjusted properly the exhaust fan only needed to turn on every 5 or 10 minutes for a minute which provided fresh air and CO2. If you keep the humidity under control a half decent charcoal filter and low fan speed can remove almost all the odors. As the filter ages, humidity goes up or the fan runs faster then you get more smell. The only way I know to go 100% smell free is to exhaust outside somehow.