Our correspondent in Madrid believes it will, as long as it continues to house the bold masterworks which the New York foundation shipped in for the inaugural exhibition.
Frank Gehry's spectacular building swirls around a central atrium, where light sloshes through glass and metal windows that leap like fish from the floor to the 165ft flower-petal ceiling. Claes Oldenburg's Soft Shuttlecock, perched on a topmost balcony, sends creamy canvas feathers cascading down the central wall.
The galleries lunge from this hub in accordance with the Guggenheim director Thomas Krens's philosophy of a 21st-century museum: "We wanted to challenge the outdated, encyclopaedic notion of a museum that leads you blindly through a labyrinth of individual examples of everything we know. That is not a post-modern, post-technological take on knowledge. Our 19 galleries are each chapters, or short stories, in an anthology of this century's visual culture," he said.
Here are Lichtensteins and Warhols that seem poster-sized. Walk through Snake, a Richard Serra installation of curved steel weighing 160 tons that sits quietly to the side of the room. It will take you several minutes. Then take a 100-yard stroll to where Oldenburg's fabulous scarlet Knifeship - a galleon-sized penknife whose blades lift and protruding oars row majestically - looks set to roll out to sea.
"The visitors can always get their bearings," said Krens about these centrifugal rooms - some futuristic in shape, others with classical proportions. This was reassuring. Like Alice, I was beginning to feel I had obeyed the instruction "drink me" and would soon be unable to embrace a mushroom.
Gehry remains unhappy about this 450ft main gallery, the one that from outside looks like a ship poking beneath the main motorway bridge entering the city. "I wanted to put walls in and make it three separate galleries but he [he pointed to Krens] wouldn't let me."
Krens insists this constitutes the building's great strength: "Much of the art of the last 40 years has been 'of scale'. It's our responsibility to respond and provide a context. No other museum could show these works as well as this building," he said this week in Bilbao.
The effect is thrilling, but the lesser works are in danger of being overwhelmed by a building that certainly fulfils Gehry's aim: "Its very important to have a museum that makes an important statement and has a presence in your life. It's all experimental. We're not precious about this. We're trying things out."
The Guggenheim Foundation has pulled out the stops for the opening of its flagship in Europe. Eight Anselm Keifers seem perfectly at home in their own gallery, whose walls curve upwards and sideways in all directions. Three-dimensional sunflower stalks and metal shards dart from the walls and the floor. Only the monochrome tones keep you from falling over.
Nine splendid Kandinskys - mercifully hung in conventional rooms - sweep from fauvism through cubism and expressionism to abstraction, complemented by Leger, Picasso, Braque, Miro and a clutch of German expressionists, with a nod to Surrealism (Max Ernst) by way of what an American critic dismissed as "two piddly Mondrians". Damien Hirst, engaging and lively, has an upper gallery to himself.
Not all these marvels will remain. More than half the exhibits will change as the Guggenheim rotates its vast collection. This was the agreement between the Basque regional authorities, who paid pounds 70m for the building, and the Guggenheim, which will supply 80 per cent of its contents.
Thomas Krens is confident that Picasso's masterpiece Guernica - withheld by Madrid's Reina Sofia Museum on account of its fragile state - will eventually be shown here.
"I fully expect Guernica to come," he said. "The Basques have paid for it with their blood and suffering. We have designed a special truck to provide the safest movement of an artwork that has ever taken place - and we'll work with the Reina Sofia on installing it."
Jeff Koons' giant Puppy sculpture, studded with 70,000 pansies, dominates the forecourt. But it was outflanked this week by a darker installation, of bouquets candles and a black-draped Basque flag, marking the spot where Basque separatist Eta gunmen shot a policeman on Monday. The policeman prevented Eta from hiding 12 anti-tank missiles, which were primed to explode at Saturday's opening by the King Juan Carlos and Queen Sofia of Spain.
Security has been tightened and the cocktail receptions have been scaled down, but the authorities insist: "nothing will make us step back" to stop the public from visiting what is already a triumphant symbol of the city.
Richard Serra: Snake 1994-96
Georges Braque: Piano and Mandola 1909-10, Violin and Palette 1909
Marc Chagall: Paris Through the Window 1913, Green Violinist 1923-24
Andy Warhol: One hundred and fifty Multicoloured Marilyns 1979
Robert Rauschenberg: Barge 1963
Picasso: Mandolin and Guitar 1924
Claes Oldenburg and Coosje van Bruggen: Knife Ship 1985. Wood covered with vinyl, steel, aluminium and motes with blades vertical.
Roy Lichtenstein: Preparedness 1968. three panels
Anselm Kiefer: Sun-ship 1984-85
Vasily Kandinsky: Blue Mountain 1908-1909 Several Circles 1926
Damien Hirst: Two Similar Forms in Endless Motion (Broken) 1993.Reuse content