So the result of me trying this without access to the Tech Tree viewer is, that I lost on the end of February 1999. I failed to deal with the cults.
However, this was mostly due to playing poorly, not due to not having access to the Tech Tree. What stalled me the most was not realizing I had to dissect a monster to get Promotion I. But since it is stated in the goals for X-Com GIB, that is my fault, not the game's.
The second thing that stalled me was not knowing I needed to research all the cult networks in order to get the Military Envoy. But that was not as bad, since I still was trying to capture and interrogate new enemies anyway. I just would have put higher priority (risking soldiers more) on it, had I known it was blocking my way to Armored Vests.
In total, while I did not win, I'd say I had a fair chance, and the Tech Tree viewer is not mandatory.
One thing I think is not adequately explained is, what constitutes Pintle-Mounted guns. I did discover that RPG launcher with Anti-Tank ammo counts, but I did not have the Ammo, as all my launchers were captured with either standard ammo, or none.
So I request that when Angry Bird is unlocked, a list of human tech weapon and ammo combinations that can be loaded onto it is unlocked as well.