No. I hate to say it, but you'll pretty much lose your settings when you set up the new device. Link it to the same account (make sure you go to https://my.roku.com/link and run away fast from anyone that tries to tell you that there's an activation fee) and all your channels will be automatically downloaded, but they'll be in a random order on the home screen and you may have to reauthorize some channels depending on who you're paying for the subscription. Anything paid through Roku should be good to go. You can just move that Roku 3 to another TV. If you decide to sell it or give it away, make sure you perform a factory reset first.
You won't have to reinstall each channel. When you link the new player to your account, it will automatically load all of your currently installed channels (along with a few suggested ones if you don't already have them). As @renojim mentioned, you will have to enter your credentials into any channels that require them.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.