No. The PS3 isn't going the way of the Dreamcast. If we go back 15 years, Nintendo was beating Sega into a pulp. Then Sony came into the picture, smacking Nintendo just as hard. This hurt Sega beyond redemption. As the PS2 came out, it had no competition. N64 and DC sales could not compare. Sega's superior competition was taken down by a stronger foe.
Now, we have the Wii selling amazing, but to a different crowd. The PS3 has sold better than the 360 until their recent price cut (When launch dates are aligned). Right now, it makes since. None of the three will die. The Wii is to one audience, the PS3/360 to another. The sales of the wii are close to the PS3/360 combined. (Which are currently close to even.
Sony doesn't have anyone beating them out of the race like the Dreamcast had. They are close to even with their only true competition. No one who wants an HD console is going to be happy with the Wii alone. Most of the people who want an XBox 360 already have one. Therefore, when the price cuts come along. People will massively buy the PS3.
Will it sell as good as the PS2? Probably not. Who knows, though. They already have all the games they need. With proper price cuts, functional firmware updates, and a stepped up marketing campaign, it could. The PS3 has sold extremely well for the price during a worldwide recession and it still has many more years.
By the time all is said and done, the PS3 will outsell the 360. If you want to ask if a console is going the way of the Dreamcast, the 360 is the most likely candidate. Everyone would agree that isn't going to happen. The only way any of the three will be taken out is if either, one of the companies goes broke (Sony of Microsoft likely), or a forth player is added to the field (Apple?).