It depends on the bait, the trap, and the dog.
It turns out that some of the dog-proof raccoon traps have two-way triggers, which is likely to make them less dog-proof than those with pull-only triggers.
And of course, if the dog-proof raccoon trap is baited with something that the dog wants (e.g. meat, peanut butter, etc.) it's less likely to be dog-proof.
As with all traps, care and discretion are called for to avoid harm to non-target animals.
Photo credit: http://l0vejamie.tumblr.com/post/32613853816