Betty, my thought is that you would need a substrate because your adhesive would just fall through the mesh. And it would probably look pretty rough underneath. Most people use a hardi backer board or ???? (can't remember the name of the other one). They both are made of concrete materials, sold in the floor tile section of Home Depot, and will stand up to the outside weather. Probably the thicker one would be best. I don't know how you would secure it, other than to screw it on.

Maybe some others have other ideas. You will hear from them soon.
BTW - Welcome.

D3 is right on using hardibacker over the wire mesh. I have the same patio table, and the holes are too wide. You could also cover it w/a layer of the wire mesh used for plastering walls, and just cut, make darts, and fold it under the rim of the table (or how about screen), and slather a layer of concrete over it and smooth it out. Make sure your base/legs to the table are sturdy enough to take the weight. Hardibacker is probably the best solution.

Or you could have a piece of glass cut for it and go a GOG...

Ramona