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.
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