No. You will have to redeploy your app in order to upload/update a static file.
But, one can easily find themselves in a scenario where you may wish to update a static file without redeploying. For e.g. suppose I changed some code in some java classes and the changes are still incomplete. Meanwhile, if I wish to change some css style or upload an image, i'll have to wait till the java classes are ready.
One workaround is that you can deploy your app(provided there are no compilation error) to a new major version. Since the static files are shared across all versions, you can see the changes appear in other versions too.