hmm, you could? But I wouldn't advise it.
Chaeto needs to tumble in a fuge. It also doesn't help if you have herbivores in your tank that eat all the algaes.
Chaeto also has tons of space for copepods to hide and multiply - so I suggest only keeping it in a fuge.
If you want a good display tank macro algae, go for halimeda, shaving brush, or a type of caulerpa (though they can co sexual!)