The short answer is: No!
Firstly, the melting point of PMMA is 160 degrees Celsius, so in order to even soften the PMMA such that it could be dissolved or dispersed in a liquid, you would need the liquid temperature to be well above 160 degrees C. Water boils at 100 degrees C, so that immediately gives a problem.
But an even bigger issue is that whilst PMMA has some polar groups along the polymer chain (alkoxy and carbonyl), the chain itself is predominantly non-polar. It means that whilst PMMA can be made to swell and dissolve in essentially non-polar solvents such as toluene, it does not dissolve in or swell easily with polar solvents, and they don't come much more polar than water.
As you will have probably noticed, PMMA is frequently used for such things as outdoor rain shelters, bus stops and so on. This is because it exhibits good weather resistance, and certainly does not show any compatibility with water.
So you can dissolve PMMA in something like toluene by heating it (and using high shear mixing), but certainly not in water.