Yes, it is my belief that government checks and balances work. I think that it is extremely important that all parts of a government go back and check each other's work because that way, everyone is on the same page and there is little room for error. Government checks and balances are essential to a functioning government.
Leavers voted, amongst many reasons, to have the UK government and parliament no longer subject to European law.
Since the UK courts have just ruled that the decision to actually trigger Article 50 is to be made by the UK parliament (giving Remainers a glimmer of hope of staying the EU, and angering some Leavers for going against the referendum), u/Victorious_Punge is hoping for the ironic scenario where Leavers are appealing to the European Court (which the UK is still subject to) to override the UK court's ruling that the decision to trigger Article 50 be a Parliamentary one.
It's like asking your parents for a ride to the bus station after you've told them you're running away.
Yes, government checks and balances work because it is the only way from letting the people decide every single aspect of government. Checks and balances are necessary in order to correct wrong decisions, like Britain deciding to leave the EU. It is the best way to avoid these horrible decisions.
The vote of United Kingdom citizens to exit the European Union was one that was misunderstood by voters and was instantly regretted by those that made it happen. In this particular instance, government checks and balances seem to be helping. However, checks and balances might not always be effective in every instance.