It does, if the friction discs in the levers are not too worn to hold a setting. just like any other friction system.The Syncro II will be easier to leave on friction mode because the knurled knob on the lever does not get in the way of shifting once it is set to friction. Also, as the function setting knob sits into well defined notch(es) within the lever body when set as friction that there is really no way for it to come off that setting other than deliberately pulling up the knob (that has quite a firm spring on it) and turning it to the indexed setting or vice-versa. Not the so with the first gen Syncro, as the second lever on the RD shifter can easily be bumped during shifting, turning it back to indexed setting which it defaults to when the two levers are aligned.
The bike that I have the Syncro II on is currently set at friction mode so at least I can ride it. It will go back to indexed mode once I figure out how to make it shift better.