It’s fine in the sense it is perfectly allowed (both in CircleCI and Docker terms). You’d have to decide whether you were satisfied that it is producing the same build artefacts between the two jobs. (Of course if you do your tests on one artefact and then deploy a different one, you will get into a pickle!)
I think I would lean towards trying workflows, given that it is probably not too much effort to implement.
The Docker pull issue is nothing to worry about - the only minor thing you may want to consider is whether the latest tag is stable enough for you. Some people pin to a specific image hash, but this is not mandatory.