HRT pretty much completely knocked out my body hair after about 3 months or so. There's still some there, mainly in what were previously the thickest patches, (a bit of chest hair, a bit of stomach hair,) but what's there is very soft and fine, and pretty much undetectable unless you really get close.
So yeah... in general, HRT will greatly reduce it. Even those I've known who didn't lose it outright generally still report it getting much softer and finer. So you can pretty much guarantee that it will at least be WAY easier to remove once you've been on HRT for a while. Once it starts becoming softer and finer, it's much less likely to irritate your skin and give you razor bumps when it pokes back up.