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Depends on the device. I have a Samsung Tab 4 with 8GB of memory, just 4GB available, but I have more than 4GB worth of apps installed, and still got 1GB free on internal memory. That Move to SD function works in my case, and I'm not even rooted."SD Card" as mentioned here actually refers to part of the internal storage. It's not the actual external SD that you insert. That button will still be there even if you don't have a card inserted in the phone.
The only way to truly move apps to external storage with Android 4.0+ is to root the phone and use Link2SD (or use a script/directly modify system files if you're adventurous).