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I'm a network engineer at a financial institution, the answer is yes if any of the following conditions are met
1. Your browser is configured to use a proxy server to access the internet (this will track where you have been)
2. You go through a content filter such as blue coats (this can be transparent to you, and again, will track where you have been. Blue coats can even do SSL proxy, so that the company has access to anything you visit over https, which is normally encrypted.
3. You go through a firewall which does deep packet inspection with the ability to do packet captures.
The financial services industry is so regulated, that I wouldn't do anything like that from work.
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