Stat boosting skills do not affect Bladetomes in general. The unit must receive a stat buff, indicated by having a blue text next to the stat attribute.
Spurs and Blow skills do not affect Bladetomes either.
Though, Henry is usually better off using Gronnowl or Gronnraven instead. Gronnblade can be used if he is consistently getting Hone/Fortify Armor buffs every start of each turn.
Which, in my experience, is very easy to pull off because of how Armor Emblem benefits greatly from being in close proximity of each other. I'm using a Gronnblade/Wary Fighter Henry that truly is a weapon of mass destruction. Who needs to hit twice when you're sitting at 80 attack value after hone/fort and +4 from goad buffs?