Yes. Exploitation of some very secure (and offline) networks have been accomplished via USB.
"noexec" and other features are not always enough to prevent keyloggers and other malicious devices from operating.
A reasonably good solution is to block all USB devices except those in a small whitelist of VIDs/SIDs (i.e. Vendor IDs and Serial Numbers). This gives you good security, as long as you guard who has access to the list of trusted VIDs and SIDs.
WINDOWS: One piece of software to do this on multiple versions of Windows is: http://www.newsoftwares.net/usb-block/
LINUX: See http://unix.stackexchange.com/questions/63199/how-to-disable-usb-devices-based-on-vendor-id-in-linux-environmenthttps://unix.stackexchange.com/questions/63199/how-to-disable-usb-devices-based-on-vendor-id-in-linux-environment