Can I list one day of volunteer work as “Month-Year”?
Well no. Not at all. What you're suggesting isn't just simplifying your resume or cherry-picking what experience to list. You're talking about substantially inflating your experience, i.e. lying on your resume.
Unless specified, listing anything on your resume as "Month - Year" will imply that you spent the majority of that month doing something. If you were volunteering somewhere for a week you'd either list it as "January - Year // Taught week-long training course for children" or, less commonly, "W3 - Year // Taught children's training course".
There is some wiggle room when it comes to rounding off months but that's only when the interval involved is long ehough. So if you officially started on the 31st of July in 2012 it's fine to list "July 2012 - March 2015" on your resume. But doing that if you left after less than a year or two would come across as misrepresenting your experience.
Lying on your resume is such an immense breach of trust that if it was discovered in the interview process you'd be immediately dropped from consideration. If it was found out after you started the job you'd risk being fired for cause in many companies but even in companies that don't immediately go that far it would be a giant black mark on your record and reputation. The only time where this wouldn't have such a dramatic impact was if it was just an honest mistake or a typo, but that would typically be discovered in an interview. If you actually lied about it during an interview, you'll suddenly have plenty of time to write a new resume.