Yes, you can do that, like this:
1 - Create a POST operation in a published REST service
2 - Use a microflow that takes a System.HttpRequest parameter
The Content attribute will be filled with the CSV file contents when someone POSTs a CSV file to that operation.
Definitely. A csv file and images and so on could be decoded to a string pasted in your request object for your service. Than you can decode it and make it again a CSV file in your published service in Mendix.
A possible application of receiving a csv file in Mendix could be like (if the file renaming and opening to CSV gives issues, you can use similar set up as in the CSV exporter module from app store) :
1 - Publish a PUT REST service
2 - Convert your CSV file to base64 data and put it in your request object and send the request object to the REST service
3 - Process the received request in Mendix by decoding the base64 data to a file and change the name to .csv and store it