seems like a good idea, though you will still have to open the HTTP port on which the ICM server listens. The exact port will depend on your installation, though often it's 8080. For added security, you might want to add a reverse proxy between the internet and your ECC system, though this is really no different to SOAP web services. Both work over HTTP so there will need to be some path from the internet to your ECC system over HTTP.
In terms of implementing the REST API on the ECC side, you have 2 options:
- use NetWeaver Gateway, which can provide OData (AtomPub) and JSON formats via a RESTful API.
- build it yourself, using ABAP HTTP Handlers (registered in transaction SICF).
Be sure to check with your SAP Account Executive whether there is a potential licensing impact. NetWeaver Gateway helps a lot with licensing additional users which otherwise don't access your system at all. You can also have a look on SCN for more info, or even check some of my presentations on SlideShare.
Hope this helps,
Sascha