Hi Far East Man!
While you can link your accounts, the two programs will still remain separate, and using the Marriott Rewards Credit Card From Chase at Starwood properties will not earn the bonus points for charges at a Marriott.
I'd highly suggest getting the SPG credit card if you plan on staying at SPG properties.
you'll earn 5 points per dollar with your platinum status and credit card combined (2x from card, 3x from plat status)
Each of those points transfers to 3 marriott points. This means you'll earn 15 marriott points per dollar when you stay at starwood properties.
It would be nice if we got bonus points from using the Marriott card at Starwood properties, but at least you get the bonus bump from matching status. Jsucool76 has a good suggestion about getting the SPG card, but I am not planning on staying at enough Starwood properties to make it worthwhile.
I just signed up and received the new Sapphire Reserve card, and that gives 3 ultimate reward points/$ on travel expenses. I can use it at a Starwood hotel and get almost as many points as using the SPG card (Equivalent of 3x MRP and 3x SPG points for plat, which in the long run adds up to 12 Marriott reward points per dollar spent at Starwood.