Are agents turned off by published excerpts?

Quite the contrary, I would think. You can find plenty of books, especially in literary fiction, which acknowledge previous publications of excerpts in litmags. And they often note that the earlier version was in somewhat different form.

The major thing that previous pubs of this sort tell the agent is that somebody out there likes your work. Which tends to make the agent like it more, too, before even seeing any of it.

caw

I imagine it would be a rights issue, since you've already sold first rights on parts of it, but I don't know how much partial published material from one book would affect the rights of the entire book. You'd probably need to speak to someone who understand copyright law to find out for sure.

I agree with Blacbird.
If excerpts have appeared in respected short fiction mags this con only increase the level of interest. The key here is respected mags, publication on your cousin's website doesn't qualify.
I don't believe the rights are much of a problem unless vast chunks of it have previously appeared