For Amazon, yes you can. You don't need to select a category to list on Amazon, since you only need a SKU and an ASIN. So you could list all of your products at the same time.
For eBay, currently you can only list to one category at a time, in order to keep any necessary data enrichment as manageable as possible. Once we add .CSV import capabilities to the Listing Builder (for bulk upload of data enrichment), we will likely make it possible to list on multiple categories simultaneously.