So all else being equal i.e. identical size, different tread pattern is a problem?
In my humble opinion, it's doable, especially if it's temporary.
is it safe? Yes, within reason. you have to understand, that it's not the optimal setup. and, if any normal passenger cars ever reach their limits of adhesion on public roads, it will not behave as predictably as if it had been equipped with all four same tires.
but at sane city road speed, I think it's passable.
I can see there being more of an issue when the replacement tire is much newer than the rest but in my situation the 3 other tires have less than 3k km on them so all 4 (three + replacement) would be of equal traction if one only considers their age and all 4 are high quality all seasons.
you are quite right.. your existing 3 tires are basically NEW... so adding 1 new tire will not negatively effect anything. (especially if you rotate tires regularly).
i think your best course of action is to : let the car sit(unless you ABSOLUTELY have to go somewhere) while you
1. see if the franchise tireshop can get that tire as he promised sometime in the foreseeable future.
2. if date's given, just live with temp tire for a bit.
3. no date, but sometime within couple month for sure? buy cheapest same size tire and keep it as spare when your new "right" tire show up.
or
3. you are feeling quite full of cash and want to try out a set of winters, just get winters. and place an order for the right tire. that way, your 3 tires are kept new, and with that new tire coming in, you will be set for next spring.
how's that?