As company policy? No. But their employees are people too.
I used to work for a large ISP that shall remain nameless. The ISP abuse department absolutely DID look at every pub ftp they were told to shut down, and grabbed whatever they found interesting before shutting it down. There may even have been a massive MP3 share on one of their servers to store their ill-gotten gains.
Absolutely NOT company policy, but it happened.
But the question here is: should OP worry about his 'linux isos' getting him in trouble. Even accounting for overly curious employees, the answer is still NO.
I'd personally feel a lot more comfortable if that drive was an SSD, not a spinning/mechanical one. Seems (and this is mostly gut feeling) like more can go wrong with mechanical drives: lubrication, things "sticking" etc.