Oil-water separation is a big money industrial process, and there are a number of methods for successfully separating the two. So the answer to your question is best approached in two parts: a theoretical answer, and a practical answer.
Theoretically, yes. A number of systems exist and the best are described below. There are off-the-shelf applications, as well as major capital infrastructure for major water treatment plants. Whether these solutions are for you will depend on your application, as well as budget. Hence, the practical answer may be different if you are looking for a cheap, backyard-employable device to solve the problem created by Granny filling the radiator through the sump oil inlet again.
Wikipedia has a very nice summary of water treatment, and includes a lot of information about the API (American Petroleum Institute) oil-water separator, which has been in effective use for decades. It is a very effective device, albeit costly, and can treat upwards of 50000 litres of water per hour. You can read about it in detail here, but I
don't doubt it is what you are after.
Something more in the lines of what you describe is the Vertical Gravity separator. It is a pressurized system which promotes separation through convection mixing as the liquid is pushed though a complex path. The differences in liquid densities encourages separation of the two components. VGS systems can treat up to 3000L per hour. A document describing the operation of this system can be found on a link to a pdf document on this page. There are some problems associated with this type of device, in that the 'filter' mesh can get blocked if the material is very dirty.
Of course, any treated water is not 100% pure, and may need additional treatment depending on your requirements.
There are a number of interesting web resources where you can read more about oil-water separation methods. Pielkenrood have an excellent page of various methods, past and present. This blog also has a number of useful pages, although it is a commercial site promoting their own preferred devices.