A good addon that helps with this is Quartz, its casting bars show when it is ok to cast another spell due to server latency. It does not however help with GCD, but your advice to hit it earlier is sound.

This is true of cast bars and Quartz is one of a handful of mods that will show the chunk at the end of the castbar to tell you when it's (probably) time to recast. I've found I can get away with going a little ahead of when Quartz says it's OK to and squeeze out an extra couple of hundred DPS on an elemental shaman.

But the global cooldown is a different beast. When you click to cast a spell, the global cooldown starts on the client side immediately and your client will reject any other casts attempts until the GCD is over without trying to send them to the server so if you're spamming an instant-cast button in the hope that it will go off early, you're wearing the paint off your keys to no benefit.

There is one trick to speed up the recasting of a GCD ability and that's to know that the game sends your casts to the server when you RELEASE a key, not when you press it. If you pick your next ability and press it down while you're still on GCD you'll be able to let go and send it immediately when the GCD finishes, which reduces your time between casts by however long it takes you to push a button down. Yes it's a tiny delay, but everything in WoW from talents to gear to playstyle is about tiny numbers adding up and this technique WILL help you close in on the cap of 40 instant abilities per minute.

I should mention that it's likely that the server also performs it's own GCD checks to prevent people with hacked clients from being able to peel off GCD and dish out faster damage, and with latency being variable you're likely to have things fail to cast if you're too precise when it comes to recasting right as the GCD finishes.

Also, if you cast something that will be rejected by the server your client will still go into GCD mode and prevent you from sending any other casts. When the server rejects the cast, the client will cancel that GCD and allow you to send the next thing. This is why casters with high latency (hello, fellow Aus/NZ players!) are better off carefully choosing when to recast instead of spamming the button - if you have a 400ms ping and you try to recast 100ms early your client is going to go into lockdown and not send anything else for the next 400ms until the server comes back saying "You can't cast that, you're already casting something", which means that your next cast will be delayed by 300ms. That's actually a biggish chunk of a spell (15% of a 2s lightning bolt, for example) to be losing regularly and will probably cost you a couple of slots on the damage meters.