Was he intending to stay on as a spy after the return of Voldemort, or planning to flee? If the latter was true, why didn't he do so after he felt the Dark Mark burn?
As others have said, because of the curse on the Defense Against the Dark Arts teachers, he likely wouldn't have stayed beyond the end of the school year. However, like you acknowledge, he could have stayed longer.
Voldemort himself notes that he didn't respond to the Dark Mark summoning:
“And here we have six missing Death Eaters… three dead in my service. One, too cowardly to return… he will pay. One, who I believe has left me forever… he will be killed, of course… and one, who remains my most faithful servant, and who has already reentered my service."
Because of his deep involvement in the plan, I suspect he didn't need to turn up to the graveyard. The graveyard scene, with the Death Eaters summoned, was about saying "I'm here, I'm back, bow to me once more". Voldemort takes the opportunity to reprimand those who had turned from him in the years since his disappearance. Barty Crouch Jr had already done his bit.
So, I think him not responding to the summons was intentional, and the plan was for him to keep up his disguise as long as possible. Remember, Harry was supposed to die in the graveyard, and it would have been disguised as your standard Triwizard Tournament death - so providing it all went to plan, Fake Moody could have stayed at Hogwarts, at least for a little bit longer, gaining what knowledge he could. He could also have taken this opportunity, and his trusted status, to quietly silence any suspicions about untoward goings-on in the maze. He would eventually have rejoined his master, once Hogwarts held nothing for him, or once Voldemort's return was known.
Had Voldemort's night gone to plan, he wouldn't have needed to leave Hogwarts immediately, and it makes sense for him to stick around and see what he can. As we see, it also works out well (at least for a bit) that he stays at Hogwarts, since it offers a backup when Voldemort's plan fails - he tries to kill Harry again (though doesn't succeed thanks to Dumbledore and McGonagall).
Crouch stated in chapter 14 that he intended to stay in Hogwarts for only one year.
"But you're behind - very behind - on dealing with curses," said Moody. "So I'm here to bring you up to scratch on what wizards can do to each other. I've got one year to teach you how to deal with Dark -"
"What, aren't you staying?" Ron blurted out.
Moody's magical eye spun around to stare at Ron; Ron looked extremely apprehensive, but after a moment Moody smiled - the first time Harry had seen him do so. The effect was to make his heavily scarred face look more twisted and contorted than ever, but it was nevertheless good to know that he ever did anything as friendly as smile. Ron looked deeply relieved.
"You'll be Arthur Weasley's son, eh?" Moody said. "Your father got me out of a very tight corner a few days ago... Yeah, I'm staying just the one year. Special favor to Dumbledore... One year, and then back to my quiet retirement."
I have a theory. I think that he was going to stay forever. I believe that Voldemort intended to kill Harry, then use his hair for a polyjuice potion, then use the portkey to go back, pretending to be Harry so that he could kill Dumbledore, then Barty crouch Jr. would stay as DADA teacher, or something. Now, to back this theory: the only portkey in any of the books that was two-way (it would not only take you to where it was going, but also take you back to where it left from) was the Triwizard cup, meaning that Voldemort most likely had some plan to go back to Hogwarts. Also, Voldemort risked letting Harry have his wand, and duel him after 15 years of being "less than the meanest ghost", which must be a disadvantage on his part. I believe that this is because he needed to be the true owner of Harry's wand so that it would work for him when he went to Hogwarts, completing his disguise. Now, you are most likely going "but why not just kill Harry?" and I say that it's for two possible reasons:
Voldemort never really understood wands. He may have heard about how if you beat someone in battle, there wand will belong to you, but not understood that you just have to win, not kill, or that you just have to overpower them, whether its in battle or not.
He wanted to prove that harry winning was a fluke (most likely of the two), and thought he could kill two birds with one stone.