It's probably not going to do any great harm, but I suspect you'll just get back another essentially template response along the lines of:
There were many good candidates for this role and we decided to go with a candidate whose skills and experience more closely matched the requirements at this time.
Thank you for your application and we encourage you to apply for further roles at the company in the future.
which doesn't really say anything either. If the company didn't have time/want to give individual feedback, it probably still doesn't.
