As all of the answers have said so far, no.

But there is another reason besides the ones given so far I am surprised nobody has mentioned.

All the existing Lockheed SR-71 Blackbirds in museums have had their wing spars broken.

I asked a museum curator this very question. I was at the Evergreen Aviation & Space Museum in Oregon which has an SR-71 on display. I thought it was one of the most beautiful things I'd ever seen, and I asked the curator what it would take to get it in the air again. He said, you can't, period.

Every SR-71 on display, he said, had its airframe destroyed before it was shipped out. They used a machine that looks a bit like a gigantic paper cutter on steroids to break the main wing supports. Those aircraft will never, ever fly again.

NASA asked the U.S. Air Force to leave two airframes intact, which they did, and those planes still flew for a while for civilian scientific purposes, but eventually they simply became too expensive and difficult to fly.

Both those aircraft are now on display, one at NASA Dryden Flight Research Center and one at an air museum in Arizona. I believe that means they have had their wing spars broken, too.

I about cried when the curator told me that. It's like desecrating a work of art.