Yes, ALWAYS tell them! The expert answer above is superb and right-on with my significant experiences involving this issue!!!
In our state, we have a Patient Bill of Rights, and are bound by law to "honor" their right to know, or to at least be told!
It is my experience, if they understand enough to show grief or loss (cry) at learning of the loss of their loved one, like a lifelong partner and spouse, the family should "honor" them by asking what THEY want to do in attending the funeral. Go to any extent to honor their request, and you will feel good and be blessed by your decision!
Make plans....if necessary, take them for only part of the funeral, and have someone close, other than family, that doesn't need to remain, and can be in charge of getting them to the service just as the family arrives, and depart with them 3-4 min. prior to the end of the service, and leave the church and take them back home where that person will remain with them until family returns from their funeral obligations. A wheelchair is also a good option even if not physically needed. It makes them less approachable/accessible by others, and easier for the person tending them to make the quickly needed exit. It is the strong emotions of others they have not seen for a long time, and the likely "not knowing" or remembering these caring and loving "faces" from long ago that can be the most upsetting part of the day for the dementia patient.
Also, as the expert refers to, honor and remember their faith and/or cultural differences. If they lived their married life in a church as a God-loving Christian couple, they would want to be at that funeral for the parting of their loved one. Honor their union and their life of Christian (or other) sacred beliefs!
Contacting professional organizations for an answer to this is the "easy" way out, and will likely only garner you a generic response, for they do NOT know your family member personally, past or present. Do NOT make this mistake!
Again, "EXPERTLY" phrased: "If it was you who had dementia, wouldn't you want to know if your loved one had passed?" AND, I'd like to add: "Wouldn't you want, if you had dementia, to be honored by your children, and be asked your wish to attend a funeral or not?" Grief is not limited to the coherent and living normal human species of life as we know it, and all of these stages of grief are just as important to the dementia patient....lest we forget, because they can't express that to us in words! This is only fair and just, for they are NOT dead!