Yes. You can enable mutual authentication for ESB proxy service. Here you want to do small configuration to enable mutual authentication for all proxy service . You can edit axis2.xml file and change following property to "require"
<parameter name="SSLVerifyClient">require</parameter>
More details you can find here. However, if you are enabling mutual authentication for given set of proxy services, There is some more to do.. More details you can find here. There was an issue with older release in ESB. therefore you need some patches to install. but with 4.7.0 and 4.8.0 (next release). there have been fixed.