
He may have already done it. I always thought the "white-out" at the corner of Asami's eye at the end of the Hong Kong arc (after he finds out Akihito is okay after being shot) suggested a tear there:
http://www.mangago.zone/read-manga/you_re_my_loveprize_in_viewfinder/mh/v05/c030/5/
Of course, it's completely open for interpretation, but considering what had just occurred it would not be out of place nor out of character.
And then there's this image that has been debated before, where it looks like Asami is shedding a tear after finding Fei Long who had collapsed from grief, outside in the rain:
http://www.mangago.zone/read-manga/you_re_my_loveprize_in_viewfinder/mh/v02/c007/25/
(If you're interested, here is the completed drawing from the book):
http://www.mangago.zone/home/photo/94795/

I don't think Asami will cry because I don't think Akihito will die now. However, if I imagine Aki's death, I would say: yes, we'd see him cry.
Asami is a human being, with feelings and emotions and some of his comments and facial expressions showed he doesn't hide everything.
Here: http://www.mangago.zone/read-manga/you_re_my_loveprize_in_viewfinder/mh/v02/c007/7/
In the French version of this page, from book 2, instead of "you're not so bad" after having said that even a top level mafia member cries at the thought of his father's death, Asami says "I respect that" so he doesn't deny that he can also cry if his heart is hurt.
And here: http://www.mangago.zone/read-manga/you_re_my_loveprize_in_viewfinder/mh/v05/c030/13/ (and even sine p.7 of this chapter), he showed everything and he was in public.
That's why, I think Asami would kill Akihito's murderer (sooner or later) and he would cry in the helicopter. A silent cry. Then when he'd be alone, he'd let himself cry openly.
The fact that he manages to accept the most part of his feelings for Akihito is one of the thing I like the most about Asami. He maybe bad sometimes but he's not so bad and he can love. It's more realistic like this.
hi guy's do wan't 2 see asami cry if something hppn 2 aki' ε=ε=(ノ≧∇≦)ノ