Can files be uploaded without HTML forms?
In theory, sure. HTML forms allowing file uploads usually make a browser perform a POST
query. (See here for some details.) Servers usually don't care how that query was created on the client side. (If they want to care, they must implement cross-site request forgery prevention measures.)
Thus in practice, this depends on your client: If it can construct the POST
request without the form, you're set.
Can files be uploaded as URL parameters instead of in the body of POST
requests?
In theory, yes, if they aren't too large. (URLs are limited in length.) Nothing in the HTTP protocol forbids you to do that.
In practice, there is probably no established convention on how to do this, so your client and your server will have to feature some custom implementation for this and to agree on the encoding etc.
Thus you can decide the format of the encoded string (as long as it's allowed within an URL parameter), but you would probably also have to implement that format on either side.