Yes, it's possible and there's a rumor that some large bars on the exchanges have been cut open and found to have a tungsten rod inside. There are some sophisticated steps beyond specific gravity that can test for tungsten cores without having to cut the bar in half... xray or gamma ray I'm not sure. It might be a sonic test - basically hitting the bar with a tuning fork and measuring the resultant ringing sound (similar to what you can do with silver). Those huge 50lb bars are out of my league so I don't pay much attention. I do know that there is a lot more scrutiny on this since the rumor surfaced last year.

As for gold coins having tungsten as a form of counterfeiting... it is not profitable for a counterfeiter to use tungsten. Tungsten's melt point is 6200F, three times hotter than gold, and requires a lot of energy to melt. Tungsten's hardness, way over 10 times harder than gold, requires much more energy to stamp the coin.

A counterfeiter won't make any money using tungsten at today's gold price. But, ramp up gold prices to $10,000 and I'm sure we'll see some attempts at counterfeiting. Just have to hope the marketplace responds with some enhanced verification tools.

As for platinum as a filler for gold coins. Historically, platinum has always been at par, or higher in price than gold so it makes no sense to use it as a filler. Only in the past few weeks have we seen gold surpass platinum in price. It will be interesting to see if this holds for any length of time.