Hello there,
Yes you can.
But running a social networking site is quite heavy and especially if you use a Social Network script like Elgg, most social network scripts out there are heavy. Running a social networking site also requires a lot of server power and resources because if you want many users to concurrently use your site then your site will likely and faster to use all server resources limit and daily hits limit. Keep in mind also that Social network needs to have a large space to store users information including pictures, videos and posts and our free plan here has a 300019 inodes limit, this limit determines how many files and folders you can upload here, the more files and folders you have the more you will likely to hit the inodes limit.
So overall, Yes you can run and create your social network (like for testing) here but it’s absolutely not recommended for production.