To be on the safe side...
Why not create an emergency 'admin' user and leave its home folder on the SSD before moving your regular user's home folder to the external HD?
If starting from scratch that is fine. However, the situations in this thread seem to indicate that there is already a fused OS X + Apps + User volume already in place.
How is the OS getting onto the new SSD drive? A bootable clone , restore from back up , or fresh/clean install ?
System restore from back-up would run into a problem if HDD content is bigger than the SSD. ( plus overhead of copying stuff on that will immediately remove. )
Some bootable cloners allow user to mark some folders outside of the process of cloning. In that case:
a. create admin account.
b. mark all the other user accounts as outside scope of cloning.
A clean install implicitly requires that the accounts be created in same order were created on the system image on the HDD ( so the user ID , UID, numbers all are consistent between old and new system. ) [ I think some folks get whacked systems when create mismatched UID and the copying between old/new volumes goes sideways. ]
Then you should be able to log in as the 'admin' user and change settings even if your external drive isn't connected.
Even internal drives can 'disappear'. If the OS disk dies and the admin account is on the same disk, it really doesn't matter much. Can't boot that OS much less login. But if the HDD dies but the SSD is OK you'll still want to be able to login and do some administrative things. ( run back up recovery, run diagnostics , etc. ). That account doesn't need a huge Photo Album, music , custom Logic plug-ins, etc.
Even if not splitting home directory locations it is still prudent to have a separate admin account and run "normal" app usage in a non privileged account. There is no good reason for normal users to run with admin privileges turned on all the time.