As long as you have your account credentials, you'll be able to log in to the new console, yes. If you want to keep your Album, you can just plug the SD card into the new Switch & it'll reformat everything but the Album for you.
There's the possibility that when migrating to the OLED your accounts might be marked as "Secondary." This shouldn't happen if you remove the users from the previous console beforehand, but if you need to, you can log in to your account on Nintendo's website to manually set the OLED as your Primary console.