During qualifying for the 2018 Mexican Grand Prix, Max Verstappen very nearly took pole position despite not setting the fastest time in any of the three sectors. (Other drivers had gone faster than him in individual sectors, but lost time in the other sectors.) Ultimately, Daniel Ricciardo pipped him to pole position by about 0.03s.
It’s hard finding the data for previous years, but the scenario you described actually happened in that same year, 2018, during the Azerbaijan Grand Prix.
According to the FIA, these were the best sector times in qualifying:
- Sector 1: Kimi Raikkonen, 35.283
- Sector 2: Kimi Raikkonen, 40.704
- Sector 3: Esteban Ocon, 25.044
It gives us the combined “perfect lap”: 1:41.031
However, the pole sitter was Vettel, with 1:41.498, who, as you can see, had no fastest (purple) sector.
As you may remember, the only reason Raikkonen didn’t make the fastest lap that day was his oversteering at T16: https://youtu.be/xMnNQOgeWJ0?t=345. By the way, you can see in the video that Raikkonen has 2 purple sectors already, the third one belonging to Ocon.