When the fixture above drains quickly, like pulling the plug and draining, it can siphon the trap below.
Will the bar sink drain slow enough? Well...........if it's really a kitchen sink with a 3.5" basket, it can drain pretty quickly. That's the same as trying to wet vent a kitchen sink over a laundry tub.
Anyway, if you are asking a code question, there is an answer for that.
If you are asking what you can do in the dark, there is an answer for that. Will the in the dark method work? Maybe....and maybe not. So much depends on the drain you're installing and how you may drain the top sink.
Is this being inspected?
If so, you can ask the inspector if he will pass that. That's what I do if in doubt.
On some commercial jobs, you always have a talk with the local inspector before you start laying out.