Would you say once I’ve read and studied through the conceptual physics book, I would be well equipped and well versed for learning fundamentals of physics without much struggle(I.e, I would then know all the basic science it assumes)?
I wouldn't say that it will save you from things being a struggle. You will be more familiar with the things you will be learning in greater depth later, but new challenge will come each level you advance because you'll be learning more technical content and learning to apply it. However, with the appropriate mathematical background you will be better equipped for Halliday. You will learn to apply calculus to situations that you'll see in physics through the calculus curriculum and then see it again in physics.