I am wondering if, for example, the view count on my post will increase when I refresh the page.
NO not this way.
If you delete all your browser cache with cookies, active logins etc. and then login again and check your question, you will get +1 visitor. Your question ALWAYS starts with 1 visitor, which is you. But you wont increase your views by simply refreshing the page. Otherwise many people had already the gold badge for 10k views, because you can create a simple firefox makro which refreshes the page every ms or whatever.