It's exactly what I did and the results were quite strange. There are only 2 self-loops, but analysis results with and without them differ too much.
Here is in-degree centrality for weighted, asymmetric, network with 2 self-loops:
navalny 76
olly_jolly 56
temkinmir 27
xenia_sobchak 26
burmatoff 24
Alexgizn 16
varlamov 15
tvrain 12
VRSoloviev 11
adagamov 10
And here is in-degree centrality for weighted, asymmetric network without 2 self-loops:
navalny 76
Alexgizn 64
temkinmir 63
olly_jolly 57
Tractorcoff 37
angeina_may 30
xenia_sobchak 26
burmatoff 24
YanaBogdanova 19
varlamov 15
I don't understand, how removing 2 self-loops can change the results so much and why they still doesn't match with the ones from NodeXL?