I can see a few different ways of doing this. It depends on the server (what software is available, how it can be accessed etc.) and the files themselves, but it can be done. One way or another.
XML, being hierarchical, is a more complex format than CSV, but on the other hand parsing it is not rocket surgery. Assuming that the file structure is fairly simple (or flat, i.e. has no nested elements) it is easy to convert it into either CSV format for uploading through the BO or into a format (CSV data or SQL statements) which can be inserted directly into the database (bypassing Prestashop completely). Or you could have a script (running anywhere) parse the XML, and send the data to Prestashop's web service. (An even better way would be to get the data from the supplier's web service - if they provide one.)
Now, adding and updating existing products is straightforward enough. The problem is removing products. To do that you would need to save a list of products before the import, ticking them off as you go. Then do a second pass, deleting or disabling the products which were NOT in the import. For that to work, you would need to import all files at once. And you would also need a way to identify the products which could be removed. (Presumably using the supplier field.)
I won't bother you with private messages - I'm sure you have enough of those already - but feel free to send me one. With a bit more information I should be able to be more specific about what can be done and how. In particular, I would like to know whether the products are "products" (in the Prestashop sense) or "combinations".