Yes it's possible.The reason your original code didn't behave like your DOT example is because NetworkX doesn't automatically use fixed positions unless you explicitly define them in Python. As @Sanek Zhitnik pointed out a graph doesn't have an orientation.

In your DOT format example, you had this:

dot
    digraph {
    layout="neato"
    node[ shape=rect ];

    a [ pos = "2,3!" ];
    b [ pos = "1,2!" ];
    c [ pos = "3,1!" ];
    d [ pos = "4,0!" ];

    c -> d ;
    b -> c ;
    b -> a ;
    a -> c ;
}

You have to do something like this:

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()
G.add_edges_from([('b','a'), ('b','c'), ('a','c'),('c','d')])

# Fixed positions (same layout every time)
pos = {
    'a': (2, 3),
    'b': (1, 2),
    'c': (3, 1),
    'd': (4, 0)
}


nx.draw(G, pos, with_labels=True, node_shape='s', node_color='lightblue', arrows=True)
plt.show()