In theory, but that would be more in the realm of philosophy. You can think hard about something you already know and deduce knew knowledge from there, but you would have no way of confirming that knowledge or putting it to a test.

In short, you end up like the ancient Greeks who could come up with a bunch of hypothetical statements, and could only assume that they were correct.

You need to read Asimov’s The Last Answer.

I think you could make a case that you could learn new forms of pure math if you had a method of storing information in your brain.

There’s that idea that your thoughts are determined by quantum particles interacting with your brain. So if you still have a body, even without your senses, you might still be able to just pull information out of the aether through this process.

You’re asking the unknowable.

Not that we can’t play along and have some fun, but that’s all it is.

I think the important part of your question comes down to what you could learn, rather than if.

Consciousness, in part, requires a progression of thought. Meaning that you have one thought, it resolves, the next thought arises, and so on. There’s an arrow of time to it. So, each thought along the way is a form of learning. It is, however, a limited form because you’re limited in scope. If the only perception possible is self perception, you can learn as much about your self as there is self to learn.

Without stimuli, a perception of external things, you can’t learn anything other than the self. There might as well not be anything but the self when you have no way of interacting with it.

Now, if you want to play woowoo with it, you might think, in this formless state, and by thinking discover that you have new ways of perceiving things, new senses in a sense. Or perhaps that you have to learn how to perceive whatever state surrounds you with your previously existing senses in a similar way to how someone that goes blind has to relearn how to use their other senses in the absence of sight. It isn’t so much that the senses no longer exist, but that the mind has to adapt to entirely new signals that it hasn’t figured out yet.

Past memory isn’t necessary to learn new things in your hypothetical state, only the ability to form new memories.

Sitting wherever you are now, close your eyes, swaddle yourself up in a quiet space. Let yourself think with as little stimulation as possible by partially blocking your senses and making what’s left as uniform as possible. In that state, the only changing stimulus (as a thought experiment) is your mind so long as you stay still.

We still learn in a state like that. Sensory deprivation as a form of meditation and inner exploration exists. And you can learn in that state. Simply learning how to exist in that state is the first thing you learn. Learning to lean into it without trying to generate sound or touch is part of the process. You kinda have to learn that to be able to explore your mind.

I would say that, within this scenario, death would serve to reduce or eliminate the “need” to crave, to chase, stimulation. Without a body providing non stop sensory signals, the mind that was once tethered to a bundle of perception via a brain would no longer be a slave to that brain. That craving for stimulation is part of why people have trouble with sensory deprivation. It’s why, in a perfect silence, we’ll hear things anyway, that humming or ringing of the ears, nerves, and brain trying to process something that isn’t there.

Our brains expect to “hear” things, so it generates a “ghost” sound akin to a dial tone.

But without the brain, maybe we would be free of that, and exist in a state where thought is the only thing that is.

Depends on what “You” is.

If:

You = Universe (as in Pantheism), then yes, you learn from yourself, you are the universe after all.

Requires external stimuli. The human brain is kind of designed to take in lots of information and process it. Interact with things etc.

One would go crazy. This would be an extreme verion on solitary confinement.

To the question. One may learn lots if untrue things.