So with this configuration, the p-trap would work properly even though the drain pipe is higher than the bottom of the sink drain?
Yes. Looking down at the drain in the sink, you may see some water a bit further down, but because the trap can be installed with the J bend flipped, it gives you the room you need to make the connection. The drain at the wall is a bit lower than the bottom of the sink. There won't be water in the sink.
A standard p-trap looks like the one below.
This Dearborn below will reverse.
I carry a few on the truck because I'm finding plenty of sinks that are too deep for a standard trap now. The fashion now is to go with deeper sinks.
The other new fashion I'm seeing, is lav cabinets with a drawer or shelf below which is too low for where the drain was roughed in at.
So sinks, too high a drain, lavs, too low a drain. It's so much fun out there on remodels.