Although it is completely safe to eat salmon after spawning, you might not want to. Around this time salmon do not eat for months on end, so the meat is therefore usually quite mushy and unappetizing. In order to get the full flavor from the salmon you catch, you will want to make sure that it is not just after spawning occurs.
This way you will be able to enjoy the full flavor of the fish and have good meat to feast on. So while you may not get sick from eating salmon after they have spawned, you will want to keep in mind that the meat will certainly be high quality by any means.