I would love to provide you a way to make this happen, but unfortunately this is not possible without coding.
Links are deprecated from wordpress version 3.5, and it's not included in the latest versions (only with a plugin), but that's not the main issue.
The problem is that links are not stored as custom post types, but as a completely different structure in a different table – thus they are not reachable for the search plugin.
The only way to make them work is to create a completely new wrapper, implement it to the plugin and design a new settings page for it – thus lots of lots of coding.Best,
If you like my products, don't forget to rate them on codecanyon :)