Acid rain is extraordinarily weak as an acid. Every change of 1.0 in pH is a factor of 10 in the amount of hydrogen introduced because pH is a logarthmic scale. Muriatic Acid has a pH of -1 (yes, the pH scale can go negative -- this is an exceptionally strong acid). So even acid rain with a pH of 4.0 would have 1/100,000th the amount of excess hydrogen as Muriatic Acid. That means it would take 100,000 times as much acid rain by volume as Muriatic Acid to have the same effect on a pool's pH. So let's say that a massive storm had an incredible 1 foot of rain added to your pool. Let's say this is a 16x32 pool is 512 cubic feet of rain which is 3830 gallons. So with a pH of even 4.0, this is equivalent to 3830/100000 = 0.0383 gallons or 0.6 cups of Muriatic Acid. In a 18,000 gallon pool, this would be a pH drop of about 0.1 if the starting pH were 7.5 and the TA were 100.
As for TA, the above amount of pH change from the acid would lower the TA by about 2 so not even measurable. However, the TA of rainwater is very low since it is in equilibrium with carbon dioxide in the air so the amount of carbonates is quite low (especially since the pH is low). Essentially, it is like adding carbonate-free water to the pool. So the dilution of the pool water by 18000/(18000+3830)=82% would reduce the TA to roughly 82% of it's original value. In practice with continuous dilution (with spillover) the reduction is less, but could be 10 or so and measurable. But again, this is ONE FOOT (12") of rain.
[EDIT] By the way, the apparent inconsistent treatment in how I did the calculations above is due to the fact that for pH there is more hydrogen ion in the acid rain (pH 4.0) than in the pool water (pH 7.5) so this is treated as if one were adding more of a substance (hydrogen) to the pool water and I ignored the dilution effect since it wouldn't change the result by much. For the TA, the amount of carbonates in the pool water (around 90 ppm) is far higher than that in the acid rain (less than 10 ppm) so I treated that as a pure dilution. [END-EDIT]
Richard