When Fred and George flew away in Harry Potter and the Order of the Phoenix, does it mean they were expelled? Or could they come back to Hogwarts later?
They would have been expelled - and worse - but they left in a cloud of glory before it could happen. And no, they wouldn't have been allowed back after that.
"I've got the form, Headmistress," [Filch] said hoarsely, waving the piece of parchment Harry had just seen him take from her desk. "I've got the form and I've got the whips waiting ... oh, let me do it now ..."
"Very good, Argus," she said. "You two," she went on, gazing down at Fred and George, "are about to learn what happens to wrong-doers in my school."
"You know what?" said Fred. "I don't think we are."
He turned to his twin.
"George," said Fred, "I think we've outgrown full-time education."
"Yeah, I've been feeling that way myself," said George lightly.
"Time to test our talents in the real world, d'you reckon?" asked Fred.
"Definitely," said George.
Had they stayed, they would have been whipped and then (presumably) expelled. But instead of waiting to get kicked out of the school by Umbridge, they left on their own, and made themselves heroes by doing so.
Think of it like employees who quit before they can be fired, in order to score points over their boss.
It's fairly obvious that Umbridge wouldn't have let them return after this, so in that sense, yes, they were expelled. Dumbledore might have allowed them back when he returned to Headmastership at the end of HP and the Order of the Phoenix, but by that time it was already the end of the school year - their seventh and final year - so there would have been no point in them returning anyway.