Not sure what you mean by non-in-memory testing but with integration testing involving an in-memory hosted web API, the requests are sent directly to the HttpServer, which is basically the first component to run in ASP.NET Web API pipeline. This means, the requests do not hit the network stack. So, you don't need to worry about running on specific ports, etc and also if you write good amount of tests, the time it takes to run all your tests will not be too big, since you deal with in-memory and not network. You should get comparable running times as a typical unit test. Look at this excellent post from Kiran for more details on in-memory testing. In-memory testing will exercise all the components you setup to run in the pipeline but one thing to watch out for is formatters. If you send ObjectContent in the request, there is no need to run media-formatters, since the request is already in deserialized format and hence media formatting does not happen.
If you want to get more closer and willing to take a hit on the running time, you can write your tests using a self-host. Is that what you mean by non-in-memory testing? As an example, you can use OWIN self-hosting. You can use Katana hosting APIs and host your web API and hit it with your requests. Of course, this will use the real HttpListener and the requests do traverse the network stack although it is all happening in the same machine. The tests will be comparatively slower but you get much closer to your prod runs probably.
I personally have not seen anyone using web-hosting and doing lots of integration testing. It is technically possible to fire off your requests using HttpClient and inspect the response and assert stuff but you will not have lot of control over arranging your tests programatically.
My choice is to mix and match, that is, use in-memory tests as much as possible and use Katana-based host only for those specific cases I need to really hit the network.
