I started watching Those Awaiting a Star despite my concerns. I am currently on ch. 15 of the manga, and I didn't have any trouble understanding the first episode. I did notice, however, certain details that would require knowledge of certain manga chapters:
Early in the episode, Ruth speaks to Chise as a dog. Later, he transforms into a boy to eat breakfast with her and Elias. Understanding this requires the viewer to have finished reading the arc where Ruth is introduced and where he becomes Chise's familiar. In other words, the viewer must have finished reading ch. 12.
Reference is made to Chise being a Slay Vega. The OVA also depicts Chise as being haunted by her ability to see magical creatures invisible to others as a child. Both of these aspects of Chise were discussed prior to the Ruth arc. (Unfortunately, I forgot the exact chapters, particularly since some of the information in question is spread out over several chapters.)
One reviewer complains that we are not introduced to Elias or given an explanation for why Chise is studying magic. Personally, I do not think we actually need to know either. As far as I am concerned, this can simply be handwaved as part of the worldbuilding or plot construction. Either way, sufficient context is given in the beginning chapters of the manga, in the first volume. The above also holds for Angelica's appearance at the beginning.
Since everything above is explained in enough detail by the point in the manga where Ruth appears and becomes a familiar, it would appear sufficient that an OVA viewer at least read the manga up to ch. 12, if not finish vol. 3. (Although Ruth's attachment to Chise happens in ch. 12, it took me until ch. 14 to properly understand that Ruth could shape-shift.)