If you have the gymnastics skill, which applies to dodge when you take a -5 initiative penalty (SR5 p.168), does the dodge specialization (comes preloaded as option in the chummer character creation program) add its +2 dice?
This section, from p.191 appears to do it,
DODGE Any character, armed or unarmed, looking for a quick, short-term boost to his melee defense can use a Dodge Interrupt Action against an attack at any point in a Combat Turn, so long as the character is not surprised (see Surprise, p. 192). A Dodge action allows the character to roll Reaction + Intuition + Gymnastics [Physical] as his Defense test. Note that since a skill is introduced to the Defense Test, a limit is introduced as well. This boost only deducts 5 from his Initiative
But this section from 168 doesn't say one way or the other,
DODGE (–5 INITIATIVE SCORE) A character may choose to use her own skill to dodge incoming attacks as an Interrupt Action (see Defending in Combat, p. 188). By decreasing her Initiative Score, the defending character can add her Gymnastics skill to the defense test. This is a one-time add, unlike going on Full Defense (below) which lasts for an entire Combat Turn.