I am assuming that you are making a web app because you refer to Apache and Node. Quick answer - Is it possible - YES. Is it recommended - NO. Node bundles it's own webserver and most websites run on port 80. I am also assuming that there is currently no Apache plugin which is supported by Nodejs and I am not sure if creating a virtual host is the best way to implement this. These are the questions that should be answered by developers who maintain Nodejs like the good folks at Joyent.
Instead of ports, it would be better to evaluate Node's tech stack which is completely different from most others and which is why I love it but it also involves a few compromises that you should be aware of in advance.
Your example looks similar to a CMS or a sharing web app and there are hundreds of out of the box apps available that will run just fine on Apache. Even if you do not like any readymade solution, you could write a webapp in PHP / Java / Python or mix n match it with a couple of ready made apps and they are all designed and supported to run behind a single instance of Apache.
It's time to pause and think about what I just said.
Now you are ready to decide on which techstack you are going to use. If your website will never use any out of the thousands of ready made apps that require Apache, then go for Node otherwise you must first eliminate the assumptions that I have stated earlier.
In the end, your choice of techstack is way more important than any individual component.
I completely agree with @Straseus that it is relatively trivial to use node.js file system api for handling uploads and downloads but think more about what you want from your website in the long run and then choose your techstack.
Learning Node's framework is easier than learning other frameworks but it is not a panacea. With a slightly more effort (which may be a worthwhile endeavor in itself), you can learn any other framework too. We all learn from each other and you will be more productive if you are working as a small team than if you are working alone and your backend technical skills will also develop faster. Therefore, do not discount the skills of other members of your team so cheaply.
This post is about a year old and chances are that you have already decided but I hope that my rant will help the next person who is going through a similar decision.
Thanks for reading.