See this enhancement issue
The short answer is yes, the groupby will preserve the orderings as passed in. You can prove this by using your example like this:
In [20]: df.sort_index(ascending=False).groupby('A').agg([np.mean, lambda x: x.iloc[1] ])
Out[20]:
B C
mean <lambda> mean <lambda>
A
group1 11.0 10 101 100
group2 17.5 10 175 100
group3 11.0 10 101 100
This is NOT true for resample however as it requires a monotonic index (it WILL work with a non-monotonic index, but will sort it first).
Their is a sort=
flag to groupby, but this relates to the sorting of the groups themselves and not the observations within a group.
FYI: df.groupby('A').nth(1)
is a safe way to get the 2nd value of a group (as your method above will fail if a group has < 2 elements)