John,
Nobody can give a hard and fast fact about this because inkjet/giclée has not been around long enough or tested thoroughly enough to provide a long-term confidence in archival permanence. I think 200 years might be drawing a long bow. How will the prints be stored? Or framed? With what materials? Matting and glass? I certainly would not strut around telling people my prints are going to last 200-300-400 years; we just do not know, and will not be here to say one way or another.
I do not have any inkjet prints pre-2010, only Ilfochrome Classic prints (raw and framed, dating back to 1978 and forward of that covering all 4 iterations of the Cibachrome/Ilfochrome print process), traditional wet RA-4 prints (early 1990s), then hybrid wet/LED RA-4 and latterly inkjet (the hybridised wet/LEDRA-4 process is slipping away as machinery and parts for these old dinosaurs are not scarce and costly to source).
Manufacturers' claims about permanence and/or image stability of inkjet over the long term have to be carefully weighted with a number of other critical factors, among them how the print will be stored, the environment and/or presented after the (printing) fact. We do know though that baryta-impregnated media is achieving considerably better archival qualities than media before it. In a way, inkjet is continually evolving and improving and we can certainly look forward to more evolution in the future.