Can a vent be started from a wye?
A couple points, some of which include what others have said.


Can a vent be started from a wye?  YES
Can you do what you were proposing? NO


As others have said, you have an S-trap there, which violates "the vent connection to a fixture drain [shall not] be below the weir of the trap" (IPC code) - the point at which air is introduced from the vent needs to be above the weir, or highest point of the seal. In your diagram, the point of air introduction is where the 45 degree part of the wye hits the drop.

You could fix this by, in effect, reversing your two connections. Instead of a wye and the 90 degree bend, use a sanitary tee to the trap and the connect the vent to the top via a 45 above to go out through your space. 

As you note, the vent then needs to extend at least 6" above the sink flood rim before going horizontally.