Yes. Funnily enough, the reflexive response of most physical scientists to this question would be “hmm, well let’s assume the Earth is flat” (which makes the answer immediately apparent).
The change in the Earth’s surface area is marginally trickier. It always helps to be aware of the line-square-cube ratio: if you multiply a thing’s linear dimensions by X, then its surface area is multiplied by X2 and its volume is multiplied by X3. So if the Earth’s diameter is multiplied by 1.0012, the area covered by the atmosphere is multiplied by 1.0024, and for its volume to remain the same, then its “height” (and pressure at sea level) must be divided by 1.0024, meaning it decreases by 120 pascals (1.2 millibars).
That change is small enough that if you were going to care about it, then you’d also have to think about the change to the atmosphere’s composition. A water-covered planet would have a considerably lower surface albedo, meaning it absorbs more sunlight, so it is warmer; that doesn’t affect the pressure, but it means there’d be more water vapor in the atmosphere (which means more clouds, which reflect more sunlight into space, so it would be hard to predict where the equilibrium would end up). A m**ster atmosphere is denser and therefore has higher pressure as a function of depth. So it’s conceivable the pressure in the Himalayas would be a little higher than it now is at sea level.
The net gravitational force acting on the atmosphere would also be smaller, meaning lower pressure, but that’d be a really tiny effect.
It goes without saying that we’re ignoring a bunch of other stuff. The levels of oxygen and CO2 would change – maybe a lot – and what with water vapor being a greenhouse gas, Earth might even go full Venus. But the rule is that if you can’t disprove a sci-fi scenario on the back of an envelope, you are obliged to suspend disbelief.
