It is possible to configure the web ssl connector to use the Windows certificate keystore (access provided by the SunMSCAPI provider). However, the JSSESocketFactory checks for a keystore file. This check should likely be skipped when the connector is configured to use the Windows keystore.

Here is what the configuration looks like:

<connector name="https" protocol="HTTP/1.1" scheme="https" socket-binding="https" secure="true">
				 <ssl name="https" 
					key-alias="jbossweb" 
					keystore-type="Windows-MY"
					protocol="TLSv1"
			</connector>

This results in an error like this:
13:54:01,821 ERROR [org.apache.coyote.http11] (MSC service thread 1-5) JBWEB003043: Error initializing endpoint: java.io.FileNotFoundException: C:\Users\imauser\.keystore (The system cannot find the file specified)

You can work around this issue by creating this keystore (C:\Users\imauser\.keystore).

More info on using the Windows keystores can be found here:
http://docs.oracle.com/javase/7/docs/technotes/guides/security/SunProviders.html#SunMSCAPI
http://www.oracle.com/technetwork/articles/javase/security-137537.html