Should I Discourage Search Engines from Indexing

Hi...
This is kind of a general WordPress question as well but I have a completely private multisite setup that I use Membership Pro 2 to protect that's on a subdomain. I don't want it indexed for any reason I can think of except that I want to use Google Analytics to track viewership. Does Google Analytics still work if I check that box that says "discourage search engines from indexing"?

I have a public site that is the root url (not subdomain) that is not a WordPress site (just html,css,javascript code and bootstrap). I do want that indexed and searchable. WordPress not indexing on a subdomain wouldn't affect the non-WordPress site on the root url from being indexed, correct?

Hope that makes sense...
Thanks