Yes !
Now, granted the situation is more complex than just that the commission can push through whatever it wants, but the following statements are true:
1) the commission can block whatever it wants (ie. it has a monopoly on legislative initiative). So it has a negative veto, and can prevent (and does prevent) anything it wants.
2) the commission can, in cooperation with the EU council, create and adopt legislation, without anything more than getting the Parliament's position (but not approval) [1]
3) they can even use other procedures to get what they want [2]
[1] https://en.wikipedia.org/wiki/European_Union_legislative_pro...
[2] https://en.wikipedia.org/wiki/European_Union_legislative_pro...
In practice the commission and council requiring each other is essentially the commission doing what it wants because it's mostly the same people, and even when not, they're necessarily from the same country and party (well, everyone in one has a counterpart in the other that's from the same country and party).
So no. The EU is a dictatorship. The commission has the only lawgiving power, and can block anyone else's initiative. The parliament ... is better paid but no more powerful than my cat ... (plus the politicians in there couldn't organize their way out of a paper bag whereas my cat has claws).
(and let's ignore the fact that the commission also controls the EU court of justice)