Beginner here but I have been doing that for a few month, I don't know if it's ok or not though. I come from a weight lifting background, so to me it just comes natural to lift weight, it's the climbing part that is new for me, and in order to not be in the gym everyday I have been combining sessions. I haven't found what works best yet though as it's pretty random what I do first, either weight lift and then climb or climb and then weight lift.

I haven't gotten injured yet, but that might be because I have been physically active for years now. I would assume that if it's someone who has not been physically active and that climbing is the among the first and only physical activity they do, that they should be more cautious about weight lifting and climbing in the same day and take it slowly.