You can definitely share a recording with the use of Google Classroom. If you are an educator, you can record a video outside Google Classroom then make sure that you will upload in on Google Drive or even on YouTube so that it can be shared on Google Classroom.
Some teachers make it a point to add some instructions to the videos too to make it easier for people, particularly the students, to understand what they have to do. If you would like to record on Google Classroom, this is definitely allowed. In fact, after recording videos, you can assign certain tasks to the students who are also connected through Google Classroom.