"On accident" (meaning "accidentally") does seem to be an unusual usage that frequently appears in opposition to the much more idiomatic "on purpose" (meaning "purposefully"). These are the kinds of idioms commonly used by e.g. children in explaining why something has gone wrong:
—"You broke my toy on purpose!"
—"No, it was on accident!".
A quick survey of the 34 incidences of "on accident" in the Corpus of Contemporary American English show about half have the sense discussed here, and "on accident" does occur in opposition to "on purpose":
HAAS: That happens in so many cases where you're got misinformation that's either leaked on accident or on purpose.
— from "Gunman Kills 32, Wounds 28 at Virginia Tech" on On the Record w/ Greta Van Susteren on Fox News, 2007
JACOBUS: Big difference when it's on purpose and when it's on accident.
— from "Dean, Democrats and Iowa's Deadline", on CNN, 2003
Other examples are from fiction:
"Dad better not see this or you'll get it. I'll tell him we were play fighting, and I slugged you on accident."
— Evan Shopper, "If I have to hit one of you, I'll hit you both" in The Massachusetts Review, 2003
She was thirteen years old, called herself a "gangsta ho" even though all her friends were white, and had already dropped out of school. "On accident," she said - she'd broken her collarbone the year before horsing around on her cousin's dirt bike and missed so much school that she simply never bothered returning.
— Emily Shelton, "From MEMPHIS (Short story)." in Chicago Review, 2003
"By accident", in contrast, has 1419 results, making it more than 100 times more common, and occurring not just in spoken and informal written English, but also in formal edited writing in academic journals, magazines, and newspapers.
This is colloquial grammar used in England, and occurs with other verbs that indicate acquisition; "steal off" and "hear off" are other common examples. It is technically incorrect from a purist's perspective, but is nonetheless in frequent use.
The replacement of "from" with "off" carries a slightly stronger sense of the act of taking, but the construction carries a distinctly lower-class sense and is to be avoided in polite or formal situations.
Best Answer
This reference puts it best:
A practical piece of advice for remembering coordinating conjunctions from the same site:
So, to answer the question -- no, the sentence needs to read: