I just started getting into BizTalk at work and would love to keep using everything I've learned about DDD, TDD, etc. Is this even possible or am I always going to have to use the Visio like editors when creating things like pipelines and orchestrations?
You can certainly apply a lot of the concepts of TDD and DDD to BizTalk development.
You can design and develop around the concept of domain objects (although in BizTalk and integration development I often find interface objects or contract first design to be a more useful way of thinking - what messages get passed around at my interfaces). And you can also follow the 'Build the simplest possible thing that will work' and 'only build things that make tests pass' philosophies of TDD.
However, your question sounds like you are asking more about the code-centric sides of these design and development approaches.
Am I right that you would like to be able to follow the test driven development approach of first writing a unti test that exercises a requirement and fails, then writing a method that fulfils the requirement and causes the test to pass - all within a traditional programing language like C#?
For that, unfortunately, the answer is no. The majority of BizTalk artifacts (pipelines, maps, orchestrations...) can only really be built using the Visual Studio BizTalk plugins. There are ways of viewing the underlying c# code, but one would never want to try and directly develop this code.
There are two tools BizUnit and BizUnit Extensions that give some ability to control the execution of BizTalk applications and test them but this really only gets you to the point of performing more controled and more test driven integration tests.
The shapes that you drag onto the Orchestration design surface will largely just do their thing as one opaque unit of execution. And Orchestrations, pipelines, maps etc... all these things are largely intended to be executed (and tested) within an entire BizTalk solution.
Good design practices (taking pointers from approaches like TDD) will lead to breaking BizTalk solutions into smaller, more modular and testable chunks, and are there are ways of testing things like pipelines in isolation.
But the detailed specifics of TDD and DDD in code sadly don't translate.
For some related discussion that may be useful see this question:
Mocking WebService consumed by a Biztalk Request-Response port