Can a water softener bypass value be used as a temporary shut off value?
Some valves can, some cannot. Yours, unfortunately, cannot act as a shut-off.

If  you're going to go through the trouble of modifying the plumbing, don't cap the line: add an inline valve on your softener line. It doesn't matter if it's before or after, as long as if you put it before, it's before the T that (you suspect) splits water to an outside tap.

There's some other ways to tell as well:


If you don't have a T that splits off between your supply line (pump/pressure tank, or municipal supply) and softener, then the outside taps must be softened.
Get some hardness test strips. These are good to have anyway, as they'll help you calibrate your softener. Check the hardness before your softener, after (eg: at a bathroom tap), and then compare to what you measure on your outside tap. It should be the same as before the softener.


Bypass valves

For the record, here's some different bypass valves:

Works as by-pass, in-service, or shut-off

Turn valves to opposite directions (one in bypass, one in service):

 

Move to "off" position:



Shut all three valves:

 

By-pass or In-service only