It most likely would depend on the SE's you're worried about and whether or not they support dynamic page variables (and whether you're using them).
Google for example supports dynamic page variables
ie.
http://mysponsor.com/tour/fhg1/?refer=myrefercode
so when it gets indexed into the search engine...the link is still using YOUR referral code which isn't a bad thing unless the sponsor makes it a point to not pay out on SE traffic.
However, if an SE doesn't support the dynamic variables it'd only track
http://mysponsor.com/tour/fhg1/
which then of course does no good for you.
You could always get around this by only using sponsors that have your affiliate code embedded in the url instead of as a variable. AEBN and Adult Players Club are examples of two sponsors that have FHGs that do just that.
If you decide to go ahead and duplicate a sponsors FHG and place it on your own site BE CERTAIN to check the sponsor's terms and conditions before doing so. You don't want to run the risk of getting your account forfeitted because they have some obscure clause about using their content off their site. While I doubt most sponsors would care as long as you're exclusively promoting them on the page it's not worth taking the risk.