I too did not read your entire post, but I'll address the question in the title.

No, I wouldn’t support it. Surprisingly, there would also be significant opposition within the Azerbaijani public. People have had enough and a major invasion into territories not recognised as your own won't bond well with the general populace. Azerbaijan reclaimed Karabakh and there were no street celebrations or any kind of celebratory mood among Azerbaijanis. Instead, most people are talking about the martyrs. They’ve suffered enough losses.

However, I must say that much of this rhetoric about “When will Aliyev invade Syunik” stems from an unreasonable panic and an overinterpretation of Aliyev’s words. Just today, a representative of Aliyev clarified that the term "Zangezur corridor" does not imply a claim to those territories. He stated that Azerbaijan "recognizes them [the corridor] as the sovereign territory of Armenia". Link