It's possible. You should take her to her pediatrician as soon as you can and get this checked. She may not feel her bladder being full or she may pee her pants before it even gets full. It could also be that she only feels it right before she has to go, and by then it's too urgent to get to the bathroom.
She may need to be put on medication temporarily to relax the bladder and be put on a pee schedule (so that she doesn't wait too long to go). If she is having frequent urination, she may have a urinary tract infection. Regardless of the cause, she needs to be seen by a doctor.
Also, be sure not to scold her or make her feel ashamed. Tell her that it's not her fault. When the doctor tells you what can be done about the problem, gently explain to her the things she can do to help herself. Make her feel like she can control this, rather than feel helpless. Until you can see the doctor, have her use the training pants to prevent too much clean-up and embarrassment.
Please write back and tell us what the doctor says. You could help some other parent with this same problem.
Also: If the doctor doesn't take this seriously and just tells you it's your daughter's fault or that she's lying, especially without doing tests, #1, get a new pediatrician. #2. see a urologist--if you can find one that treats kids, that's even better.
