"Do the images generated by the free credits have a watermark?"

Yes, If you are using a free plan the watermark will be applied to a downloaded image. 

If you don't mind having a watermark on something you would create commercially, then feel free.

Just note that you should not attempt to remove it.

If you would like having a downloads that aren't with watermark, consider subscribing to a premium, individual or all app subscription to Creative Cloud