We've never seen Akou lose his composure so it would be interesting to see if he'd go on a suicidal rampage. I could see it, but i don't think it's a guarantee. Obviously, the nature of Ousen's theoretical death would be important. I believe if things happened well beyond Akou's control, he wouldn't blame himself and would go independent.
One could argue that we actually know the least about Akou's personality/mentality of all the current Ousen army commanders.
I think A Kou is the most predictable of the bunch. Everything about A Kou's character indicates he longs for nothing more than Ou Sen's approval.
He reads to me as a more dogmatic version of Gyou'un. Loyal to a fault, even if it costs him his life or pride. If Ou Sen recruited Shin or Mou Ten and appointed one of them to #1 vassal, A Kou would likely keep his mouth shut, he wouldn't act out so to speak. Certainly not in front of the others.
I don't think a suicidal rampage would necessarily be in the cards if Ou Sen died and A Kou failed to prevent it. I imagine he'd either be dead already or fall into total shock before eventually committing suicide days/weeks later.
A Kou is not the type to judge himself fairly. He judges himself by what he perceives to be his master's standards, and I imagine that demands perfection, if not the closest thing to it. Barring illness, losing his master is not something I think A Kou could survive. I do not get the impression at all he would be interested in being his own man. Perhaps he'd answer the call, similar to A Kou and CGR, to avenge his master. Perhaps he too could be persuaded by Ou Hon to serve him instead.