Carpenter ants are what I'd be worried about--I had a bunch of them that were living in one of the old pallets I hauled in the garage to burn,and they migrated to the rear endwall,and proceeded to chew the hell out of the header over the overhead door opening,they ate part of the 2x6's and tunneled into the layer of plywood sandwiched between them...a good dousing with used motor oil laced with gas,fixed that issue..
They also found some 3x12" planks I had stacked on a work bench--one day I heard some strange noises coming from that area,and when I picked up one of the planks,it was light as balsa wood--the underside was just tunnels and sawdust,and about a 1000 ants!..

--some of the ants were over an inch long,and could bite !..
I also found about a million more of those huge black ants living behind a piece of hardboard I had lying against the steel arches,and they had made a nest at the bottom of the arch,there was so many ants I had to use a shovel to pick up the thousands I killed with gas and carb cleaner..
I learned not to store any more firewood inside the garage that I can burn that day,and to chuck in any wood in the stove right away I suspect might have ants in it...

..several of the huge cherry trees in my yard have been taken down by those ants too--one barely missed hitting my car when the tree broke in half,about 8 feet off the ground...