Hey again. I haven't given my villagers anything other than clothes but I can confirm after designing their houses they no longer put clothes you give them in there. They can however add in diy tables or cooking stations that take away what was placed there temporarily. They usually put the house back the way you designed it after they're done but one time Tangy left the stove out for a while after she finished cooking.
I've given Etoile plenty of gifts after I redesigned her home, and so far she's displayed none of it. I also redesigned Raymond's about a week ago, to match his default house, except I left a bendoid on his desk. Again, since the redesign, none of the gifts I've given him have shown up in his house. So to answer your original question: in my experience, I'm gonna have to say no, it seems like they don't.
They don’t add new items. However if they need to craft or cook, if they don’t have a workstation or a kitchen, they will replace some items around temporarily. Once they finish their task, it reverts back to its old self.