Last Epoch will support both online-only and offline-only characters at release.
The online version of the game will be server-authorative to minimize the cheating that occurs and maximize the cheating we detect and subsequently deal with. As with the rest of the game, the multiplayer is not yet completed. Throughout beta we will ramp up testing from internal testing, to friends & family, to community people under NDA, to the general beta population.
We'll be wiping characters at release - and once a character is played offline, that character will never be playable online. I can't claim that there'll never be any cheating - not sure any company can - but we'll always do our best to give our players as much information as we can so that they can make an informed decision about what they want to do, and where they wish to do it.