In short, not always. Some chemicals prefer not to exist as hydrates in the crystalline state. For example NaCl or NH4NO3. They may absorb water from the air, but that does not get incorporated in their crystalline structure. Others may normally be hydrates, such as CuSO4.5H2O, but they may lose the crystalline water on exposure to air. Still others may exist in several shapes, containing no crystalline water or several different molar proportions of it. E.g. Alabaster, CaSO4, and gypsum, CaSO4.2H2O, and they may not be readily interconvertible by just sitting out there in an open vessel. In your case, both MgCl2 and MgCl2.6H2O are deliquescent, so the first will convert to the second in open air, but the adsorption of water will not stop. So you can never really be sure how much water, crystalline or not, you have there. This particular chemical is quite user-unfriendly that way.
No. Many chemicals are hydrophobic and do not bind to water. Additionally, there are a large number of chemicals that react with water. I'm sure other people can come up with more reasons or exceptions.
In short, not always. Some chemicals prefer not to exist as hydrates in the crystalline state. For example NaCl or NH4NO3. They may absorb water from the air, but that does not get incorporated in their crystalline structure. Others may normally be hydrates, such as CuSO4.5H2O, but they may lose the crystalline water on exposure to air. Still others may exist in several shapes, containing no crystalline water or several different molar proportions of it. E.g. Alabaster, CaSO4, and gypsum, CaSO4.2H2O, and they may not be readily interconvertible by just sitting out there in an open vessel. In your case, both MgCl2 and MgCl2.6H2O are deliquescent, so the first will convert to the second in open air, but the adsorption of water will not stop. So you can never really be sure how much water, crystalline or not, you have there. This particular chemical is quite user-unfriendly that way.