Will the Canadian geese on our river pathway be cool if I sit with them?

I've started biking to work on a public river trail and there's usually a couple dozen geese that are just waddling around. I think the park ordinance says I can't feed them because they're a nuisance?

How do you know when they're nesting or otherwise more hostile? Are there certain seasons where they are more defensive?

So far they haven't hissed or anything, but I think it would be cool to sit on the bench and hang out with them, but I don't want to piss them off. I don't know anything about geese except people always say they're nasty. I think they're pretty, though, and they look kind of cute padding around the park.