BlackSheepTwoOneFour
No. Too many empty boxes in the house is considered a fire hazard. I put mine in the recycables.
Styrene isn't exactly something I would want exposed to flames either.
If secure fire proofing is the goal, store the kits in air tight metal containers.
As for me:
I try to eliminate as many boxes ( and styrene sprue ) as possible.
Rarely do I keep even NIB kits in their original form.