I did that last year when we were going through the temp issues on the PRU. I even made a special tray for the cold packs and dual muffin fans to push air across the ice packs and into the intake under the heat exchanger. It didn’t solve the problem because the air wasn’t spending enough time in contact with the ice to cool sufficiently to cool the air enough for the GF.
It needs a larger volume of ice than a few ice packs. Or a/c for the room or even focused on the GF intake.
There’s a whole thread out there (probably in Made on a Glowforge) about the design of my ice pack cooling system and experimential results.