You can say that.
While Divine served the royal family in the palace, Shadow would have been in the tomb, guarding the artifacts. So, yes, Divine would have been somewhat lonely without her sister present, and that Atem's father might have sent her to teach his son the aspects of life during his childhood.
Also, what if Shadow pitied Ryou Bakura for his vulnerability towards the Thief King? Since she is technically responsible to ensure that the malevolent entity is supposed to leave his alone, what if she willingly and temporarily took his Ring into her possession? Plus, she does have a long, difficult history with Bakura's spirit, what if she temporarily was under his control?