I do have a webcam permanently plugged into my home desktop, but it's a model with prominently lit LED trims whenever it's actually on. Now, if you insist, I'm perfectly willing to believe that some combination of vulnerabilities does exist that would allow someone to re-engineer and/or switch its firmware (or driver) to snoop with no LEDs lit but I believe it would take some serious doing - with that kind of attention that webcam would be the least of my problems. Hooking into some IP-cam's open ports with default credentials is one thing - this would be quite another.
Then again, if there's money in this, maybe I should start selling in-line USB dongles that do nothing but monitor current to a webcam and beep whenever it suddenly goes up. ...Naaah, I'm too lazy. Shenzen, are you listening? Free product idea...!