My brewing experience is pretty much close to zero, so I usually spend my time just reading posts, never replying. However, as an avid fish keeper, water chemistry is something I can chime in on.
Coming from that perspective there is one fast and firm rule - never guess always test!
I just wanted to clear up some terminology. pH, Alkalinity, and Hardness are all three completely different things. High pH has no scientific correlation to alkalinity or hardness and vice-versa. pH is a measure of the hydrogen concentration. Alkalinity is a measure of the ability of the water to store excess hydrogen in a bonded form that can free itself when free hydrogen is absorbed elsewhere. Alkalinity is best thought of as a measure of the ability to resist a drop in pH. Hardness is a measure of the concentration of dissolved mineral ions.
"Hard water" is associated with the Hardness measurement. Hard water can independently have a high or low alkalinity, and can independently have a high or low pH. By definition the three things are not related. So measuring pH will not tell you anything about water hardness. You would need a separate test to measure hardness.
Another important note is that boiling will not reduce the hardness of water. The minerals will not evaporate out. The carbonates in the water can evaporate, but only by an amount equal to the ratio of water that evaporates, which is pretty much zero. The alkalinity of boiled water can decrease (and therefore so can the pH) but once cooled it will go back to what it was before assuming the original measurement was taken correctly and no other minerals were introduced as a result of the boiling process.
Lastly, in the presence of an ion source (easily found already existing in the water, or in the pipes that carry water, or even in a well), higher temperatures can lead to harder water as more mineral ions are "picked up".
One more lastly. Lastly, due to the delivery system of tap water it has increased susceptibility to dissolved gases. As a result any water parameter (pH, Alkalinity, Hardness) should be measured after the water has been outgassed, usually after suggested time of an hour. Otherwise the measurement may not be accurate. Give it a try. You will probably see at least one, if not all, of the parameters change if you measure out of the tap vs. an hour later.