No, there won't be a notification when the chain is up to date, but you can tell because the node will only be importing 1 block every 15 seconds or so, instead of hundreds at a time. If you want to be sure you are fully up to date, you can just check the block number reported by your node against a blockchain explorer.
How long it takes can vary from hours to days depending on your hardware and network connection. You can watch the output to see about how many blocks/second you are syncing, and compare that with the number remaining to sync (as indicated by a block explorer)