Would GDP for a pure endowment economy be equal to zero?
GDP would not be zero in endowment economy in general. There are still prices and also interest rates, savings and investment in endowment economy. First, lets ignore other countries because foreign aid complicates GDP calculations (as Art pointed out if the endowment is foreign aid GDP would be zero). So lets suppose there is only one country, lets call it Arstotzka, which has an endowment economy (i.e. production is fully exogenously given).

A simple macro endowment model of economy would be the following.

There is one representative individual with following utility

$$u = \sum^T_{t=1} u(C_t)$$

where $U$ is the utility, and $C_t$ is a consumption at time $t$. Standard assumptions apply $U'(C_t)&gt; 0, U''(C_t)&lt; 0 $, that is utility is increasing but at decreasing rate.

Now this will be an endowment economy so lets assume initial endowment of $A_0$ and additional per period endowment $Y_t$. 

Logically consumption must be equal or less the endowment, but rational consumers will always use up their whole resources (in this model there is no inheritance) so I can set it as an equality (this just simplifies the math):

$$\sum^T_{t=1} C_t= A_0 + \sum^T_{t=1} Y_t$$

This problem gives us the following lagrangian:

$$\mathcal{L} =  \sum^T_{t=1} u(C_t) + \lambda \left( A_0 + \sum^T_{t=1} Y_t - \sum^T_{t=1} C_t\right) $$

First order conditions are given by:

$$u'(C_t) = \lambda \implies C_1 = C_2 = C_3 =... =C_T $$

This means that the consumption will be same in each period because marginal utility of consumption is constant.

Hence we know consumption will be $C_t = \frac{1}{T}\left( A_0 + \sum^T_{t=1} Y_t \right) $ 

Furthermore, assuming no government and hence no public saving the saving is by definition just difference between endowment income and consumption at time $t$ $S_t = Y_t- C_t$

Now lets parametrize our model. 

Lets suppose we only have two years $t=1,2$. Next the initial endowment is set to 0\$ (to simplify calculations) and the per period endowments are $Y_1 = 60\$ $ and $Y_2= 40\$ $ 

Hence consumption based on the above solution will be $C_1 = 50\$, C_2=50\$$ so in period 1 there is 10 dollars of savings and in period 2 10 dollars of dis-saving $S_1=10\$ $  $S_2=-10\$ $.

Now GDP using consumption approach would be in period 1 $Y = C + I + G = 50 + 10 + 0 = 60 $ (since $I=S$  which is the same which you would get through the income approach as by our set up the endowment in $Y_t = 60\$ $.

To sum it up GDP wont be zero because endowmends are income. In real life on a tax return it would be some windfall profit but regardless thats just semantics. In real life pure endowments dont exist so we dont really have a name for them in accounting formulas but the point of income approach is to add whole income of a nation regardless of how you call the source of income as long as it was produced withing borders of a country for GDP. For expenditure, approach you again just add all spending in an economy again regardless of the fact that spending was based on purchasing some some endowment output $Y_t$ or actually produced through some inputs.