A quick question while thinking about it, can the orc warriors on a siege bow, or a great beast as a matter of case, be upgraded to warriors of Dol Guldur? The upgrade mentions "you can upgrade any number of orc warriors to orcs of Dol Guldur at a cost of +2pts per model" and the crew of both the great beast and siege bow state they are warriors. Has this been FAQ'd?

I'd say no to both of them.

Regarding the siege weapons, those are not regular orcs. They are somewhat special since only those orcs can use a catapult or a siege bow.

As for the great beast, is different than the mumak. The player chooses whatever he wants to fill the howda, and then pays the price. The Great Beast has 9 orcs with bow as "equipment" already and they cannot be upgraded or switched.

Basically, in both istances the player does not field common orc infantry, but models limited by the special rules of the siege weapon/great beast. Since neither the siege weapons nor the Beast allow, by themselves, to upgrade their own crew, it should not be possible.

Edit: I think I overexplained and made a mess. Basically, Siege Weapons and Great Beast special rules overrule the common rules

Great beast is a no. It's in the official FAQ.