It's my understanding that gaining links through reciprocal arrangements don't carry as much seo weight as one way backlinks. Assuming this is true would it be advantageous to block the links page on my site using robot.txt so the search engines wouldn't see the reciprocal links?
People viewing the cache will see what Google sees (i.e. no links). You could stop Google caching the page, but that will make some people suspicious.
Savvy webmasters search Google for their partners links. AFAIK there's no way to cheat on that.
Look at it this way: if all the people linking to you did what you're thinking, what would happen to your site?