It is possible if you have a keytab, AND the login process is not configured to save the TGT.
The way the login is supposed to work is that the users ticket is just a byproduct. It isn't the goal.
A kerberos login works by:
0. get the users login identity (and sometimes principle name - otherwise use the login identity)
1. Asking for a TGT from the KDC (which requires the users password to decrypt).
2. Getting a service ticket for the local machine
3. Decrypting the service ticket using the host keytab
4. if steps 1-3 succeed setup the users session
5. save credentials
The users TGT (and the cache) are the byproduct of step 1. It requires code to save the ticket (it is stored in a memory resident cache for use in all three steps). Only after step 3 is completed (and the user account is set up) can the users credentials be copied to a user accessible cache. Step 5 is optional.
At this point it depends on the utility you are using to login (it may not allow saving), and the /etc/krb5.conf file:
I'm assuming you are using PAM for the login. Some systems (such as RH and RH derived systems) put the users cache in odd places (/run/user/<uid>/...) so things have to be compiled appropriately, and the users KRB5CCNAME has to be set by PAM. (see the reference file for how to retain cache entries...)