I suspect that this description of Queen Alexandra's jewels for a Court held in March 1903 may fit with the description of the Cartier jewel, but it does not give us any clues about the look of the necklace.
The Times 21 March 1903 p. 12.
On 14 June 1902 p. 12 The Times also reported that Queen Alexandra wore at a Court an Indian necklace of emeralds, rubies and diamonds but there was no mention of pearls.
On 7 June 1907 p 10 The Times carried a similar report
But without some images, I find it impossible to decide what her jewels might have been.