Don't see why not 🙂 Plants do manage to survive in 'the wild' without CO2 being pumped at them and someone rushing out with a sunshade at regular intervals!
Viewing would be tough, but then some tanks look pretty cool from the top and there are always snorkels 🙂
You'd have to pick plants carefully, so they'd survive in the temperatures/conditions they experience, native plants would be a good option. Maybe have a look at some biotopes for inspiration - they are often based on what you see in a pond or lake but then carefully scaped. It would be a good way to do a native biotope on a big scale. Eleocharis parvula is a UK native so would be a good option for a pond here. Eleocharis acicularis ( the bigger version) is often sold as a pond marginal.
Another thing to be careful of is some plant species are invasive, so make sure you aren't introducing anything to the outdoors that's banned or could be spread and cause problems.