I think it's possible, but it's likely to take weeks or months. The packs absorb/release moisture slowly. (They can release more than they can absorb, which is why they're better for low RH environments).
It's humid here in Roanoke, too. Virginia has had an unusually wet year. It's going to stay humid until a) the weather pattern changes or b) it cools off, which won't be potentially until late September.
If your towel ain't drying with the AC on, you are going to have high humidity issues. Since you're a grad student with atyical college living arrangements, you might want to consider a dehumidifier from the Lowe's in Christiansburg.
