You DO order what you want. Sullivan's nod only helps "tip the scales" in the server's favor- if you have a strong aversion to ordering it (ex: you can't afford it, you have an allergy), then no, it won't affect your choice.

The only reason I can think of for SN working over the phone is the seller feels more confident using it- which transfers to the listener in their tone of voice.

And don't tip poorly because your waiter/ waitress uses the SN- they're just trying to get you to try something new & enjoy your visit... & hopefully this becomes a better tip for them, yes. Don't you want a better paycheck too?