I am an undergrad student and I am going to sit for placements next semester. I plan to do a project on my own (without supervision by a professor or anyone else) during vacation.
Even though it isn't a project officially done for school or work, is it appropriate to include it in my resume?
Yes it is acceptable to put projects that you do on your own on your resume. In fact it's standard practice. Make sure that they are worthwhile projects, and be prepared to talk about them and ideally provide code samples.
The projects you make are the only ones which count in an interview, well you made them as an employee or as an enthusiast are two different things and they need to be handled differently.
Yes if your project has potential it will count.
Handling Personal Project
With personal projects you have to really own what ever you do and choose, You cannot just say it was client requirement or my Tech lead asked me to follow this approach. You have to be prepared to justify technically any third party library you have used or design pattern you have used. If you want to start on a project and intend to show it on resume make sure it is best of your effort and "your effort" part is more important.
At my university, you could not get credits for your personal projects. When i'm understanding the question right, you just want to add them to your resumee - which is completely fine.
