No. This comes to the question of how long is long enough.
Right now we're facing a climate change challenge because of the higher degree of CO2 going into the atmosphere. Let's say in 200 or 300 years we've established technologies that provide a balance between our CO2 emissions and what the earth can absorb, and our CO2 levels decrease in the atmosphere. There's nothing wrong with the CO2 we're putting away now leaking in the future. It's just that we have to be in balance in nature with our CO2 emissions and what the earth can take on.
Some people have suggested that, yes, we have to monitor this for 10,000 years. Our civilizations haven't even lasted that long, so far. I think the more common thinking is perhaps 500 to 600 years when we are more in balance with our CO2 levels within the atmosphere.