Is ELK designed to handle many queries at the same time ?
Yes. If you hit at some point a limit, you can increase the number of replicas. All primaries and replicas are serving searches.
Then have a look at some elasticsearch users: Github (I believe many users are searching at the same time), Wikipedia, Uber...
query is not that intensive ?
It depends. Really. It depends on what you are doing and how. So you need to test your scenario.