Well, let's see how we can try to calculate that. First of, we need to find out what is the mass of the column of air on Mars and then find out how much mass the sublimation of ice will add to it and what the effect on atmospheric pressure will be. Also, we will need to study a bit the water phase diagram.
But we will start by evaluating the possibility of sublimating all this ice.
Can we even sublimate all this ice?
At any moment in time, Mars receives between 492W/m² and 715W/m² of solar radiation (in space, before being filtered by its atmosphere).
This received energy is absorbed in part by the atmosphere, another bigger part by the ground and the last part is sent back to space (Mars Bond albedo is 0.25). This means that for every hour, on a square meter, the received energy from the Sun (if the atmosphere would not absorb energy) is at most 1.931MJ (in the summer, on the most favorable latitude).
To sublimate the ice, it's necessary to add 2 590 600J per kilogram of ice. So, every hour, you would vaporize 745 grams of it. Our 10 cm layer of ice weighs in at 100kg, so to sublimate it completely, it would take you around 135 hours, which is much more than 24h39m (the length of a martian sol). And whatever you'd sublimate during the day would just transform back to ice during the night.
It's thus impossible to sublimate all this ice.
But hey, let's check if it can have an impact on the atmospheric pressure anyway.
So, let's start by studying the phase diagram for water!
What's important to note here is the location of the Solid/Liquid/Vapour triple point. It's set at 273.16K and 611.657Pa.
Also, very importantly, if we want liquid water, we will have to be at a temperature above 273.16K, almost regardless of the atmospheric pressure. (The lowest temperature at which we can have liquid water is 251.165K and 209.9MPa).
Regarding what we just learned, it's unlikely having a huge variation in atmospheric pressure will lead to a climate change with a positive impact regarding the availability of liquid water.
What would matter most would be a temperature change.
Let's also have a quick look in the meantime at Mars climate.
We can see that in summer, the temperature regularly go above 0°C with maximums at 30°C recorded. However, since the atmosphere is so thin, there is very few dampening, so the day/night variation is quite high, in the range of a 100K (so -80°C at night, and 20°C during the day).
If you want you can stop reading there: the day/night variation is too high to keep any water liquid through the martian night. So yes, there probably is some water in a liquid state during some days around the equator, however, it's not flowing long enough to have a measurable impact on the climate.
Now, let's see how much pressure the sublimated ice will add to the air.
Little reminder, the average atmospheric pressure is basically the weight of the column of air (martian air throughout this answer) over the surface.
The average atmospheric pressure on Mars sits at 600 pascals, but raises to 1155 pascals down at the bottom of Hellas Planitia. 1155 pascals is 1155 N/m² so this means the total weight of the air column over a square meter in Hellas Planitia is 1155N.
Interestingly, this is above the water triple point. This means there could already be liquid water in some places on Mars without needing to sublimate the underground ice.
Mars surface gravity being 3.711 m/s², the mass of this column of air is then 311.24kg.
Let's say the ice is spread out evenly over Mars to a 10cm layer of ice. This would be 100kg of ice on this square meter. If it's fully sublimated, this layer would be in the atmosphere, so the mass of the column of air will be 411.24kg, which on Mars is a weight of 1526N, so a pressure of 1526 pascals on the ground down at the bottom of Hella Planitia (an addition of 371Pa, or an overall average atmospheric pressure of 971Pa).
The problem we have is that the range of temperature at which the water stays liquid at this pressure is quite low, about 0-10°C.
So, in average over Mars, sublimating all of the ice would not lead to a very significant change in atmospheric pressure regarding the formation of water.