In short, I think not.

There are two potential factors here, the Neville that we know, and how he would have been changed if Voldemort had killed his parents. We'll assume his mother died for him as Harry's did for Harry, and so he survived.

First, Neville as we know him. I think, as brave and nice as he is, he does not have the initiative, ability, or deep friendship with Hermione and Ron to destroy Voldemort as Harry did. I don't think Neville would have been able to get out of all the scrapes Harry did (although I suspect he wouldn't have gotten into as many to begin with, and that alone could have prevented him from having the opportunity to destroy Voldemort). I don't think he could have taught Dumbledore's army. And, most importantly, I don't think he would have left school to track down all the horcruxes. He just wasn't that sort of person.

And second, what would change if Voldemort had "mark[ed] him as his equal." Neville grew up being raised by his grandmother. That probably wouldn't have changed. He wouldn't be able to see his parents over holidays, and if anything I think that would make him less confident, with more anger and, therefore, less control. I don't think Voldemort destroying his family directly would have made him a more able wizard, and I think the prophecy would not have been fulfilled because I don't think Voldemort attacking him would have made him his equal.

For the timeline with Neville's parents, we go to book 4, inside Dumbledore's memories. Four people (Barty Crouch Jr; Bellatrix and her husband are not explicitly named but are two of them; and I'm not sure who the fourth is):

The four of you stand accused of capturing an Auror - Frank Longbottom - and subjecting him to the Cruciatus Curse, believing him to have knowledge of the present whereabouts of your exiled master, He-Who-Must-Not-Be-Named
...
You are further accused... of using the Cruciatus Curse on Frank Longbottom's wife, when he would not give you information.

Shortly thereafter, Dumbledore pulls Harry out and explains:

The Longbottoms were very popular... The attacks on them came after Voldemort's fall from power, just when everyone thought they were safe.

In short, I think not.

There are two potential factors here, the Neville that we know, and how he would have been changed if Voldemort had killed his parents. We'll assume his mother died for him as Harry's did for Harry, and so he survived.

First, Neville as we know him. I think, as brave and nice as he is, he does not have the initiative, ability, or deep friendship with Hermione and Ron to destroy Voldemort as Harry did. I don't think Neville would have been able to get out of all the scrapes Harry did (although I suspect he wouldn't have gotten into as many to begin with, and that alone could have prevented him from having the opportunity to destroy Voldemort). I don't think he could have taught Dumbledore's army. And, most importantly, I don't think he would have left school to track down all the horcruxes. He just wasn't that sort of person.

And second, what would change if Voldemort had "mark[ed] him as his equal." Neville grew up being raised by his grandmother. That probably wouldn't have changed. He wouldn't be able to see his parents over holidays, and if anything I think that would make him less confident, with more anger and, therefore, less control. I don't think Voldemort destroying his family directly would have made him a more able wizard, and I think the prophecy would not have been fulfilled because I don't think Voldemort attacking him would have made him his equal.

For the timeline with Neville's parents, we go to book 4, inside Dumbledore's memories. Four people (Barty Crouch Jr, Bellatrix and her husband are not explicitly named but are two of them, and the fourth is Rabastan Lestrange):

The four of you stand accused of capturing an Auror - Frank Longbottom - and subjecting him to the Cruciatus Curse, believing him to have knowledge of the present whereabouts of your exiled master, He-Who-Must-Not-Be-Named
...
You are further accused... of using the Cruciatus Curse on Frank Longbottom's wife, when she would not give you information.

Shortly thereafter, Dumbledore pulls Harry out and explains:

The Longbottoms were very popular... The attacks on them came after Voldemort's fall from power, just when everyone thought they were safe.