My experience with China Airlines & Alitalia Elite+ number travelling on KLM is that my number is well in the system but it doesn't recognize you as such. Meaning you won't get to see that you are allowed extra luggage neither does it show you that you are Sky Priority. On my BC (after printing it at home) Sky Priority is shown.
But in the case I wanted to bring 1 bag on a intra-EU flight the system wanted to charge me for it. I called KLM customer care and they solved it ( that time).

I asked it in the AMS lounge one time and the agent told it was normal all that, besides with my Alitalia card I did not have the rights for a better seat selection ( I just have to pay).

Long story short: accept KLM not giving you any Skyteam Elite+ benefits in advance but at the airport they will after all.

ps. checking your TA flights on DL website, when opening your file you may see that DL system recognizes you as Elte+ (although in the KL system not)