No, the European Commission is not democratically elected and I have no reason to think they’ll pay any attention to the concerns of the public.
I know that this is the wording the EU itself chooses to put there, but no. They are not "voted upon". Parliament cannot choose a EU commission president. The council (the heads of state of the member states) put forth a candidate and if the parliament says no, the council has to select a president (this time ... without the parliament needing to confirm them)
Like anything else in the EU, the executive is in full control of
1) itself
2) law in the EU (the commission is the ONLY EU institution that can make laws, and yes, the essential part of that is that the parliament IS NOT in charge of EU law. It can neither force a law through nor can the EU parliament prevent the commission from enacting a law)