No.
Oversimplifying the flag system into "downvotes" is unnecessary and will produce unwanted effects.
Flagging a post or comment is done for specific reasons, and should be a very rare occurrence. People upvote sometimes just to show agreement. Changing the flag system to "downvotes" would encourage those people (a majority of the users) to use them to show disagreement.
Currently, we tend to show disagreement by commenting and laying out our thoughts. With the proposed change, many people will skip commenting on things they disagree with (after all, that will just get you downvoted), in favour of just leaving a downvote.
Flagging is for inappropriate content, direct attacks, and not too much else. We shouldn't encourage overuse of that by calling them "downvotes" and changing the warning popup.