I'm not sure
On the surface of the water the weight of the atmosphere is applying pressure. This pressure is also driving the water into the straw.
Inside the straw the elevated water has weight, and is trying to fall downwards.
The height of water in the straw marks a state of equilibrium: the force of the atmospheric pressure and the force of the weight of the elevated water + the pressure of the enclosed air at the top of the straw are equal.
The water level in the glass (apart from the straw) has dropped due to the now missing elevated water in the straw.
I still expect the pressure in the glass to drop.
I'm not entirely sure...
The pressure at the bottom of the glass will be: (weight of dropped water level + atmospheric pressure).
The pressure at the bottom of the glass underneath the straw will be: (weight of dropped water level + weight of the elevated water + reduced air pressure in the straw).