^^^^
I don't think so, otherwise a family friend I know would have been in trouble. I think they do share information on criminals and such, but not on your ordinary average citizen or PR, there is no reason for the U.S to inform Canada when their Greencard holder enters the U.S or vice versa. Canada also has no exit records.
Take it for what its worth and I guess it depends on the border officer, a family friend of ours had both a PR card (now a citizen) and Greencard in 2003.
Never had any issues, there was no stamp or anything as she just showed them her Greencard, you are allowed to enter U.S with Greencard only if driving in.
Anyway now she is a CDN citizen, and her application for U.S citizenship has been approved and she has to go for that some time this year for the oath thing.
When she goes to U.S she uses her Greencard and Lebanese passport (if flying in), and comes back to Canada on CDN passport.
She always filed U.S taxes, has a bank there, and she went there every 6 months, she also had that 2 year rentry permit thing just incase there was ever any trouble.
I dunno hiope it helps, good luck.
Generally Americans are more strict in terms of keeping your Greencard, if you are out longer than 6 months they will ask you a lot of stuff, in terms of Canada they don't seem to be t hat strict. This website is full of people who were out for a long time on their PR card and had no issues coming back in. As long as you meet the minimum rules for Canada ie 2 years out of 5 you should be ok. Its the U.S guys which are stricter, I think the fact that you work and live in the U.S will help you keep your Greecard with no problem.