My friend Russ Worthington has made a cousin relationship table, and is even adding his cousin relationships to an Ancestry Member Tree, and using the Hints to try to support the cousin relationships that he receives on the mobile app. See his blog for more details - https://worthy2be.wordpress.com/.
I haven't gone that far, but I do usually click on the lineage for the purported cousin and see if it makes sense to me. In some cases, I have gone into FamilySearch Family Tree, Geni.com and WikiTree to determine if the lineage there is the same, and if the lineage "looks right." Ideally, each step in the lineage should be researched, but I don't want to take the time right now.
I do check the line that the app shows for my lineage, and in several instances it has added one or more generations and found ancestors that I do not have in my Ancestry Member Tree. When that happens, I look closer at the purported ancestor of mine in the records. I have not found one new ancestor doing this yet - almost all of the relationships that I don't have in my tree cannot be supported by records and good judgment.
I now have over 50 cousin relationships from the mobile app, and I cannot recall what I've investigated, so I made a cousin relationship table in Microsoft Word from the app information, and added a comment column so that I know what I've investigated.
Here are three screen shots of my tables:
As you can see, I have questioned the information of 8 of the relationships. I probably need to be more consistent in my comments.
Only 11 of my common ancestors are from my mother's side of the family, and all but two of those are from New England. However, three of them are in my "Unlikely" category. My father was from New England so that makes some sense. Maybe I should color code the grandparents line.
What else should I add to this table? It is for my own use so that I can keep track of what I'm getting, and I probably won't add to the table forever, but it's a start. It took about an hour this afternoon to make and if I get 10 to 15 new cousin relationships each week, adding them will not be an onerous task.