(Disclaimer: I learned about aphantasia from this question (or the one before it). I'm sure there are others with more informed experience. Also, from a few minutes of Googling it seems that aphantasia, like other neurological traits, exists on a spectrum and everyone's case is different. So... maybe the only way to know for sure what your personal experience will be like is to experience it!)
As far as I can tell, it absolutely doesn't have to stop you, but it can present some challenges. After all, much greater challenges could be overcome; someone deaf from birth could certainly learn music theory, and I could imagine them even composing brilliant works. Your challenge is more on the scale of "could a dyslexic person compete in a spelling bee": certainly; they'd just have to work a bit harder.
Really, this question could be posed as "just how does internal audiation help in music theory or performance," and then figuring out how to work around the absence of those helps. Music theory is mostly analysis; it's taking musical material and explaining it. By the way, if you're curious, here's a good overview of what's covered in the course and exam (assuming you mean the U.S. AP system).
It summarizes the activities under four main skills:
| Skill |
Description |
| 1. Analyze Performed Music |
Apply musical terms, concepts, and relationships to performed music (aural). |
| 2. Analyze Notated Music |
Apply musical terms, concepts, and relationships to notated music (written). |
| 3. Convert Between Performed and Notated Music |
Apply conventions of musical notation and performance in converting music between aural and written forms. |
| 4. Complete Based on Cues |
Complete music based on cues, following 18th-century stylistic norms. |
"Analyze performed music" means you'll hear a bit of music played and have to identify things about it. This might be very specific, like "here is a multiple-choice option of three notated versions that vary in rhythm or pitch; which one was played," or perhaps broader like "was that a full cadence or a half cadence." In these cases, you'll be able to hear the audio example, so you won't have to "imagine" the notes from scratch. Where you might have a disadvantage compared is, after hearing the example played, someone without aphantasia could keep "replaying" the music to themself as they consider their analysis. If your experience lets you "replay" the immediate memory of a phrase then you're in luck; if not, I suggest jotting down whatever shorthand notes about it you can while it's playing.
"Analyze notated music" is right in your wheelhouse: all the information is on the page. Inner audiation would still be an advantage here; we often learn intervals, chords, etc. by focusing on "what they sound like," and someone with inner audiation could look at the example and imagine that experience, just as an actor could read lines and imagine the timbre and diction with which they would deliver them. But you can absolutely look at two notes and calculate their interval by counting the half steps between them, whether or not you hear it. I always advise people to learn music theory at a piano keyboard, and to play every example. I suspect that hearing it as you learn could still be of some value, at least in understanding concepts like pitch space on an experiential level, even if you can't replicate that experience on command.
"Convert between performed and notated music" means either that you'll hear a bit of audio and be asked to notate it (or to fill in a partially completed notation), or that you'll be given notated music and asked to perform it (in ways that don't depend too much on performative skill, like clapping a rhythm). You probably apply similar skills with language. If you can read written language out loud, or take dictation as someone speaks, these are just the musical equivalents. They may be more challenging since you've worked with spoken language since birth and written language since only a few years later, and most people have less experience with music notation. But any prior experience you already have will help, and you'll train these skills during the course. If you lack inner visualization as well as audiation, this could be a disadvantage during dictation, as someone else might hear an A and imagine it on the staff. But while this person has a shortcut, as long as you can distinguish up and down and relative distance, and accustom yourself to the sounds of thirds, fourths, fifths, etc., you can take dictation.
"Complete based on cues" might seem like the skill that would challenge you most. This means you'll get a fragment of music and be asked to add to it. But this is not "free composition" subject to your own whimsy; the test is looking for you to have a working knowledge of a number of "plug-and-play" conventions. For instance, if you get a four-bar phrase that ends with a dominant chord, you would probably follow it with another four bars, quoting the same melodic material, but altering its ending to cadence on the tonic. If you become familiar enough with the tools, this doesn't require "inspiration," just knowing which tool to choose.
