Not with Links as far as I know. Definitely not with a standard install - possibly with a plug-in, not that I have seen one.

You would be better off using something like Fluid Dynamics Search Engine. I have installed it on a few sites and with some extra configuration it can be set up to do full-text search on PDFs (and Word documents too). It's not free but it is excellent value.

You can set the search engine up to re-index the site via a cron job every so often. If you wanted to incorporate this with a Links install it would work best if your site was using detailed pages.