Is the warranty on my new Omega valid

The quick answer is no. If Ippo are not authorised and the card is identifiably stamped by a grey dealer then I think you might struggle unless Omega did it under goodwill. That said, my experience suggests it all depends on the representative you speak with and whether they bother to check the status of the selling dealer. I have had a warranty repair on a 4 year old Omega I bought second hand in the UK with a card stamped and dated in Japan. I couldn't really make out who the dealer was as it was very blurry and I don't speak Japanese, but Omega honoured the warranty based on the date on the card and the watch was repaired, serviced and the warranty extended. This was handled by a boutique with whom I have a good relationship so perhaps they did me a favour but I suspect it is luck of the draw.