The kind that is screened on all 4 sides? No. You'll have no way of keeping the humidity where it needs to be.

How's your humidity there? I never did anything special for mine when I was in NC. Water in a bottle cap or sprayed down the sides once a week. If your climate is naturally high in humidity, you might be fine with mesh.

Could also do an exoterra or one of this as other options if you are trying to have something that looks nice.

I would recommend a simple 10 gallon tank with mesh lid.  It definitely has the security, ability to retain the right amount of humidity and heat.  If you use sterilized soil, eco-earth or similar substrate, if you place it in the bottom of a screened enclosure not only will tiny pieces fall through, but it won't retain the right humidity because the substrate will be exposed to the air constantly.   I also recommend using spaghum moss to retain the right amount of moisture.  Good Luck!

I will disagree with you slightly on the 10gal tank suggestion, for an arboreal species they need vertical height. A 10gal can work, but it needs to be stood upright, which will make a screened lid useless. For that a piece of plexie can be cut to size. A 2-3" piece at the bottom as a substrate guard with another piece for the rest of the length attached with hinges. Really for a smaller Avicularia species you can do a 2.5gal tank setup in the same manner.

Some of my larger arboreal species were actually getting their toe hooks caught when I tried a metal screen cage. I would have to imagine a soft screen would be even worse.

Exo Terra's are great for T's.

Whatever they said because I know nothing about tarantulas.  Award me points.  Please close your question - thank you!

Hey I just met you. And this is crazy. But award some points. Close this question, maybe?