Can you buy DLC in Steam and it shows up in your game through Origin?

Hi! I have seen a lot of people ask if they can transfer their Origin games to Steam - but few have asked about the other way around. IOW, can I buy an Expansion pack for The Sims 4 on Steam even though I only have the base game and the expansions I currently own through Oirgin? 

If I buy for example Get together on Steam, download it etc., and then later open my game in Origin - will Get together be there as a pack? 

The sale on Steam ends on the 9th, so if I do not get any answers before then I will try to buy a stuff pack to check if it shows up as installed in the game. 

To make it clear once again: I am NOT interested in redeeming the games I own on Origin through Steam, I am interested in knowing if you can buy DLC through Steam and it will show up in the game even if it is bought through Origin.