I don't know whether GG would be suitable or not. Have you consulted a reputable nursery in your area or possibly the extension service out of Texas A&M?

I found the attached link. Open the link, go to the bottom of the page and click on the Palm Tree. In the table that opens Thuja spp. is listed under both Medium and Large Shrubs for all coastal areas. Other plants you may want to consider would be some of the various junipers or Arizona Cypress depending on how much room you have to play with.

Good Luck

Here is a link that might be useful: Landscape Texas Coastal Areas

Thank you very much for your responses. I consulted two nurseries in the area and both of them were of the view that the GG doesn't do particularly well in Houston. I would appreciate other suggestions for privacy screens.

Eastern Red Cedar comes to mind. It usually has dependable cone/pyramid shape if grown in full sun. It can take moist soil if well-drained.
Other possibilities would be some sort of holly or standard arborvita, but I have no experience with these.

Thanks Scotjute!

My Thuja Green Giant has grown very well in the Houston area. I started it as a 1 gallon at 14". Two years later its 8ft in a 20 gal pot. I will plant it in the spring. It looks somewhat like a full Calocedrus decurens.