The crickets will chew the fibreglass screen. Maybe not today, maybe not tomorrow, but soon, and for the rest of your cham's life...
Seriously though, there are a few things you can do to prevent/minimise the damage:
1. Cup-feeding. Not an ideal solution, because part of the reason you get the fine fibreglass mesh is so that you can keep the insects in and free-range them.
2. Don't let crickets stay the night. This is very important. Make sure there are no crickets left in the cage overnight. They're quite active when it's dark, and when they've got no cham hunting them down, they have all the time in the world to get to work chewing on the fibreglass screen.
3. If you do get one or two holes chewed through by crickets, they're usually quite small. What I've done in the past to patch up the hole, is to dab a small bit of aquarium silicone on the spot. It bonds the mesh together, and forms a small patch when it is dry. After patching many holes, this will become a bit unsightly, and you'll have to replace the whole screen, but if you're just patching one or two small holes you'll hardly notice it.
If you want to see just how effective they are at chewing through the fibreglass mesh, just try using it on the lid of a cricket container... In a few days, you'll have crickets running around everywhere, and quite a tattered looking lid on your container...
Why do you say that? I would say that there are pros and cons to both types of screening...