Not talking about what you can place, but what you can have added to your inventory TO place? Generally, if it's of no broker value or vendor sellable, I donate for the pittance of prestige. However, the other day as I was donating something like my 75th floor grate or small vase, I started thinking, "is there?" As we have no way to remove items we've added, I'd sure hate to get to a point where I go to consume or donate an item, then find I'm at my limit...and stuck with my 75+ floor grates to deco with for all time. I'd guess there is not, but I also would have guessed the ignore list was uncapped....till I hit my 1001st ignored gold seller/vertical spammer.
Can't say I've seen or heard of a limit on the base item inventory. I've done a LOT of donations to my league hall (tons of signage from Doomed Metro lol) and I haven't reached a limit or gotten any sort of message that I can't donate anymore. Plus I've got one character getting a lot of Atlantean stuff and she hasn't seen anything like that.