Is it acceptable under an Agile philosophy to have the dev do the testing and the code to lack unit tests?

I don't want to rant, but: I've just joined a new company as the only software developer there. I've heard the promise of a fully Agile methodology and bought it.

The Head of IT now tells me that they "don't have time" to do software testing so that it will have to be me who does both the deving and the testing. Even more, the current codebase, which lacks any unit tests and is not even testable in most places, is planned to be delivered before unit tests are put in.

Does this still adhere to Agile methodologies? I know every company is free to mutilate the core principles to their heart's desire, but would any Scrum master call this acceptable?