The safest answer is that if an outside enterprise (be it an employer, client, free public library connection, whatever) supplies any part of the resources necessary for you to do whatever it is you're doing, they can and likely do monitor it - and in many cases will control it.

And it depends on the business the enterprise is in. I am now retired, but my current part-time employer (golf) allows us to go to every golf page in the world, eBay, ESPN, etc., but I cannot go to Yahoo Games - or any games site for that matter. No online poker for me - damn! :-)

My previous employer (IBM) was much more lenient, but on the other hand, had many more tracking programs in place. Strictly following the rules was a condition of employment.

So, the bottom line is you take your chances......