The definition of “safe” is relative to your theme and other plugins.
I test every off-the-shelf plugin in a local development installation first to check for PHP errors, memory usage, activation/deactivation problems, Leave No Trace score, and general compatibility with other plugins and stock themes I commonly use.
Looking at the code for this plugin, you will see it simply flips a switch that enables link manager. The link manager module within WordPress has not changed since 3.5 when they, for some reason, disabled it by default.
By the way, I reached out to @nacin to ask if he could update the readme to indicate this is still compatible with 3.5+ but I have not heard back.