Is it possible?
Of course, it is. You just might need to do more work managing your trust material and initializing the SSL context for your application. You can choose to trust one and only certificate, or you can choose to use trust material shipped with JRE and then selectively add trust material specific to your application.
You could use SSLContextBuilder from Apache HttpClient 4.3
to simplify the process of trust and key material management and initialization
is it acceptable in production environment?
This very much depends on the security context and requirements of your application. Trusting only one specific certificate without trusting any of standard CAs might make your application marginally less susceptible to man-in-the-middle exploits but will require re-configuration and possibly redeployment every time the certificate in question expires or gets revoked. It will also become your responsibility to ensure that the private key will not fall into the wrong hands. It is a combination of pros and cons.