Town or entrenchment recovery bonus for leaders?

[Brett Nicholson]

If the attackers in an assault in a town hex have an unmodified morale edge then they should get a +1 column adjustment to use against the -2 for being in a town. Similarly they might be eligible for the combined arms adjustment, the leader adjustment and/or the engineer adjustment. So, for example, in 1944 a US engineer with a Sherman and a leader of any sort with morale superiority would attack on the 24 column. (DF 9+5=14, column modifiers -2 for town, +1 for combined arms, +1 for engineer, +1 for leader and +1 for morale superiority).

I understand that but was concerned whether attacking units also get a recovery bonus in a town hex during an assault or if it is exclusive to only the defending units that occupied the town hex first. I understand the shift on the assault table for being of a higher natural morale.