I was thinking about it, but chancing it 4 years ago when I started heating with wood. I try to keep the bin filled, 110 cubic feet, and keep a decent stack, about 2 days worth near the stove. We never had any but a stray spider here and there, nothing any other house wouldn't have. The only problems I had with pests was when my wife thought it was a good idea to feed the outdoor critters, and keep all the food, peanuts, corn, birdseed, etc. in the garage. It took me a year and 7 bags of rodent poison blocks to get them out of my attic. The other one was I had a pile of extra mulch left over from the year before, decided to use it in the front landscape beds, and we got an infestation of centipedes. They were trying to escape the hot sun, so they came into the basement. But never had a problem with ants, spiders or anything else that would live in firewood.
We put 4-5 cord in the basement. Have done it in this house for over 30 years. Never noticed anymore bugs than the ones that fly in the house when you open the door.
^ this. I don't believe there are all that many bugs in firewood in the first place and the few that are/might be there really don't survive the environmental change of outside to inside. The only bugs I'd be worried about are the powderpost beetles and they're supposedly gone by the beginning of Summer and are only in the wood the first year of being stacked. At least that I've seen. I've only had termites in a small tiny stack of firewood once and I threw most of that wood out.