The ants won't die from that type of treatment, but spiders and crickets and other pests should, if you use enough bombs and block off all the openings so the insecticide doesn't escape. Make certain to leave windows in your house open if you don't want the poison filling up your house too. And remove all pets and cover aquariums (turn off pumps/filters) or you might kill those too.
For ants, the bombs might deter them, but since ants live underground, 90% or more of their colony will be unaffected by that type of treatment. You have to set out baits for the ants to eat and carry back home to wipe out their underground numbers.
Many insects hide in nooks and crannies, and crickets hide during the day, and wander about during the night (in my experience). Finding openings in your house and sealing those should keep crickets out. Check seals along doors and in the foundation.
For ants, set out baits. Try making this homemade recipe:
1 tsp. boric acid powder (often called Roach Proof or something like that, you can find it with pest products in a store like target or wmart)
2 tsp peanut butter
1 tsp honey
Mix all together until smooth, then take little pieces of cardboard and put a smear on each piece. Set the bait along ant trails, inside or outside. The ants will congregate on it for a few days, then taper off. The honey attracts sweet loving ants, the pnut butter attracts protein loving ants. Every few days renew the baits, or whenever you see ants. Gradually, the boric acid will kill the colony.