The title is pretty self-explanatory. The 2 bonus AC when "Near Death" does trigger, but not the +2 attack bonus.
In this case this is my lvl 5 fighter with 15 str in expertise mode. Without any weapon feat, he normally has +2 attack bonus (in expertise, 5(BAB) + 2(STR mod.) - 5(expertise)) and should've climbed to +4, but didn't.
Keep up the hard work.