Does homeowners insurance typically cover insect damage?

I came home the other night and noticed some saw dust under a large picture window sill, and saw ants crawling in and out of the molding. I removed the molding and sill and found that they had colonized inside the frame of the window and destroyed it (and who knows what else under it) I'm wondering if my homeowners might cover the damage since it'll be much more than my deductible. My estimate is roughly $1500-1800 since the entire window will have to be re framed (thermal pane) some drywall work, the alum flashing on the exterior, paint, and maybe some studs (if it's bad enough).