The answer is No, as stated already. The reason WHY is because you have not one, but two rules applying here.
One rule says "You can assault after Running."
The other says "You cannot assault after a Deep Strike."
So, which solution breaks no rules?
If I assault, which rules am I breaking?
Fleet: Not Broken.
Deep Striking: Broken.
BZZZZZZZZZZZZZ! WRONG!
If I do
not assault, which rules am I breaking?
Fleet: Not Broken.
Deep Striking: Not Broken.
Therefore, the only way to not break any rules is to not assault.