Having owned an eco-sphere for 3 years I'm sure it's possible to an extent. However, what you need to remember is that the conservation of matter is important within a closed system. Therefore, you need a very complete ecosystem to sustain one for a while. There needs to be enough total nutrients and minerals in the system to grow the inhabitant to its full potential. You also need to foster a culture of denitrifying bacteria to keep nitrates down and alkalinity up. If you don't have denitrification going on, then your nitrates will climb, your pH will fall, and you will get "old tank syndrome" and ammonia will rapidly accumulate.
Keep in mind that the organisms in your system can't accumulate biomass (for very long) without the addition of organics to the system. Take aquaponics for example: you have fish and plants growing in the same system. Often, some of these plants are fed back to the fish. However, you can't expect to just pull plant and animal biomass out indefinitely so the fish are fed other things such as pellets or insects (depending on region and availability). So you can't expect fish and plants to keep growing in a closed system unless there is an additional input of nutrients. The goal is mostly to maintain biomass equilibrium, with the plants and animals maintaining a typical weight. That's one of the reasons you never see these ecospheres with young fish. They try to reach equilibrium with an adult animal that doesn't need to assimilate as many nutrients into biomass.