Is it possible?

is it possible to grow a plant like this?

Not really, you're not going to be getting enough oxygen to the roots

we call that 'hydro' but you would need a running water system under it, or some way of getting fertz and nutes to it. the roots need oxygen so putting it into a sealed jar would just kill them. but you have the right idea. look on this site for hydro growing, that may help you.