Is it safe to remove "Google app" from android system completely? I rooted my device and I removed some obvious bloat-ware, such as Cardio trainer (I bike to work, I definitely do not need that), some Google music, Google books, Google maps and many other Google XXX and Samsung XXX consumer applications.

Now, in second purge iteration, I'm looking at apps that are big but their purpose is not obviously blatant.

One of them is "Google app". The name isn't very informative. Does it manage my link between android and Google account? Or is it some search service? What is that app and what are the consequences of deleting it?
Sure you can iff the Google app has the "G" logo, it is just a search app. I am on a custom ROM, Cyanogen Mod 13 and it doesn't come with bloatwares or Google apps.