At this level of politics he may read some from time to time or read all of them, but the more likely thing is that staff reads them -- especially if that person has a significant number of notifications. Just depends, but I'd say the chances of him seeing an individual reply -- as you noted -- is quite low. But, the overall "tone" that some people are disappointed may get bubbled over to him.
However, I think it is pretty clear why he said what he did regarding Moore. Battle is running for Governor. His back-and-forth with Kyle Whitmire and subsequent "debate" (which he decisively won) and the Moore support is clear indicators of political calculation. Why else would someone mix it up with a Birmingham News personality that wrote an article about Birmingham? Why else would someone like Battle endorse Moore. Answer: He's running for Governor, and he knows that if he didn't back Moore that 75% of Moore voters would never forgive him. However, 90-95% of people that don't like Moore, but have positive sentiments for Battle, Conservatives, or the GOP, are likely to overlook it given time. If Battle ends up in field with a number of Moore style candidates/loons then what are we going to do? Vote for the loon? That Battle is making these kinds of political calculations right now fits perfectly with the political cycle for the 2018 Governor's race. What's interesting is the coincidence with the regular election for Sessions' old seat. If Moore wins the election in December (which seems almost certain), then Battle can't waver on supporting Moore because Moore will be on the ballot next to him in 2018.
That's just my read of the situation. It is analogous to why so many in the GOP did what they did in regards to Trump, and only those that were retired/retiring or no longer holding public office are really to hit him hard -- outside of a very select few.