From what I've gathered, yup, pretty much. 

But I am sure others can add far more information than me. My knowledge is much more limited than most here. 

Also I believe the last block reward is around 2140, but don't quote me on that. 

poe7645

So there will be no block reward but transaction fees as reward for miners.

akhil

bitcoin

When Bitcoin becomes a global currency?

Mining won't stop when the last bitcoin is mined well after my time on this Earth. Therefore mining will continue and the miners paid in transaction fees, which if by your assumption one sat being as much as one Bitcoin now. Should be enough to incentive for mining to continue well beyond when the last sat is mined from the block reward.