Hello Jerome,
Yes we do support resumable uploads on signed URLs, but it requires a little bit of extra work on the server-side. I've written this up on Stack Overflow for posterity:
The normal workflow looks like this:
* Client requests a signature so it can do a PUT
* Server does authentication and returns a signature
* Client does PUT with the returned signature
The resumable workflow looks like this:
* Client requests a signature so it can do a PUT
* Server does authentication and returns a signature
* Server returns both the signature and the upload ID to the client
* Client does one or more PUTs using the provided signature and upload ID
Benson
Google Cloud Storage Team