It depends. At some point you'll need to start learning songs to progress. If you're very early on and very patient you could continue to grind the basic lessons for a while and start when you have a few more tools to work with.

Personally I find it speeds up my progress a LOT if I learn something and then apply it somewhere else (in different songs, rhythms, etc.). Usually that's time well spent and I can come back and perform a lot better in the original exercise than if I spent the same amount of time just repeating it.

By not learning songs you risk a couple things:

1) Not really dialing in the skills you've covered in the lessons (see above).

2) Getting bored. What fun is this if the only song you can play is "Lesson 2A"?

3) Not developing your ability to learn songs - if your ears (in terms of figuring out melody/chord changes) and reading ability lag significantly behind your playing ability then learning new songs will be frustrating and slow until you catch up.