Submitting to a journal as an undergrad but lying about academic status on bio

It's maybe too easy to offer advice on such matters when one doesn't have to live with the consequences, but for what it's worth: for your own peace of mind, and to minimize the risk of long term consequences (while possibly increasing the short term risk, though not by much I hope), I think you should send a contrite email to the editor explaining what happened and apologizing. Although there is no telling for sure what the editor would do, considering that your bio status is immaterial to the acceptance decision, I doubt that this will cause them to unaccept the paper. In any case, it's the right thing to do. And if you decide to stay silent and keep your deception a secret, you will have to spend the next few years worrying that it will be discovered, with potentially worse consequences for your career. Nip it in the bud is what I suggest. Good luck!

As a professor who has trained a lot of graduate students (and someone who still recalls what it was like trying to get started in research), I would echo the answers by Dan Romik, Laurent Duval, and Chris John. It might sound like a relatively harmless and justifiable fib, but I guarantee you that if discovered later, it will be seen as a serious blot on your reputation, simply because it suggests that you are prepared to lie to secure a publication. You might never contemplate falsifying results, but people cannot know that and suspicion of your integrity can be fatal to your career.

The good news is, that if you own up before publication, and admit it was an error of judgement, there's a very good chance the editor would be lenient to someone just getting started. Everyone makes mistakes and odds are good he or she was once an eager undergraduate too!

Scientific conclusions in papers may turn untrue, models or data can be wrong. But at the heart of research, intellectual honesty seems to me to be a core value. One should not state something he knows is false. @Dan Romik gave the sounder advice.

Lies are "a little" like bank accounts. Sometimes they get unnoticed in offshore paradise islands for a whole lifetime. Sometimes they get unveiled with compound interests and the necessary prejudice. A little lie at one time turns into tremendous cheating after a few years.

The only situation that could save a little is: would you be a PhD candidate when the paper is published? I believe as @Dan Romik that a status should not be an acceptance reason. But then your bio would be factually correct. And for the sake of honesty, a footnote under your name stating that:

"the author was an undergrad student at the time of submission"

would be nice addition. Indeed, papers written by undergraduates can get noticed, because it can mean early orientation toward research.