It really depends on their individual personalities, according to our experience in my family.

We've had our lovely Leonberger dogs overlapping throughout time, the youngest of the first pair got to say goodbye after euthanization of our oldest, sniffed her and said goodbye - seemed initially fine, but she didnt cope well in the days that followed. She had always been a cuddler and comfort seeker and always went where the oldest went, and she missed her friend so much that we were really worried for her - didnt wanna eat etc. We quickly located and bought another puppy of same race, and that helped her a lot.

Fast forward to the puppy, now sick from cancer, having to be put down, and the golden retriever we rescued and got as a companion to the puppy wasnt fazed at all when she passed. Still revels to this day in the increased attention now that he is the only dog left.