In “theory” (no pun intended): no.
In reality: some basic theory is needed.
Don’t confuse it with knowing how to read sheet music though.
If you want to carbon copy existing solos, you don’t need theory.
If you know some theory though, you will learn how the solo is built upon its underlying chords, how you can alter the solo to your taste and why some notes will sound better.
As soon as you want to step up the carbon copy solo, you should at least know a shape in a scale. Justin Starts out in his courses with one shape in the minor pentatonic scale (in A) and one shape in the major scale (in G). Knowing these two shapes in the not-so-coincidentally chosen keys, gives you a primer to your first improvisation. That means; making your own solos! The minor pentatonic is often used in blues and rock and even with only one shape in your fingers, you will have an essential tool in your toolbox.
As soon as you get a bit comfortable in a shape and tried some improvisation over a simple backing track, you will find that you answered your own question and know that you can’t do a specific specialty without a broad base of basic skills built under it.
See it as a pyramid. On the bottom you have your basic skills.
On top of that more advanced stuff and on top the specialties like “epic soloing”, “fast playing”,“squealing pinch harmonics”… it’s the stuff on top that impresses you the most…at first.
BUT it’s actually the broad base that lies beneath it that becomes your toolbox for music.
I’m not saying that you should learn all the possible basic stuff first but try to work as a pyramid: every time you add some basic stuff on the bottom layer, you can add a tiny bit of it on the layer above it.
As soon as that second layer has some stability as well, you can start to work on some “specialty” above. In the meantime, your base layers need maintenance and further expansion for more stability.
In another thread, I already explained that you can use this method for building a song repertoire as well, with basic knowledge of chords and structure in the base layer, nailing the riffs and lyrics and putting n the details and solo’s on last. Thy to have a broad base layer of songs of which you can fluently play the chords with but in the meantime, build a pyramid so that you have 1 song you can perform after a while.
I’m not forcing another “education” method into Justin’s lessons here, it’s merely one way to approach all this magnificent content; a pragmatic approach to learning with variation, challenge, comfort and of course; results that you can show. up to you to decide how you want to build your knowledge.
Justin’s method already is kind of incorporates this concept as the lessons don’t let you learn theory for a year first. try to go through the beginner and then intermediate course and have a taste of the different flavours the “base layers” offers you. If you feel there is more to playing guitar than building a narrow tower of skill towards epic and fast soloing, you will take a huge step forward in the mentality towards the passion that unites us all here ! 
Good luck!
), and I don’t know if later on Justin recommends when to enter into this topics as he did with ear training and music theory.