Lol no they wouldn't. That would never happen. Coaches are petrified of change and breaking groupthink. Just look at the complete unwillingness to go for 2 points prior to the 4th quarter or go for 4th downs ever. Cleveland has lost two games this year, Dallas and Philly, because of their coaches terror of going for 2 prior to the 4th quarter. a 5 point lead is functionally identical to your chances to win as a 6 point lead. If you are up by 5 and have the option to kick an extra point or go for two, going for two is the right choice even if you only convert like 28% of the time since your opposition is in a nearly identical hole whether it is 5 or 6 points. Carolina has blown at least two games this year because of their refusal to go for 4th and 1 late in games. It cost them in the Atlanta game, it cost them a couple weeks ago. The miniscule field position gained by punting is worthless compared to the potential in running out the clock. Carolina has one of the best running games in the league and won't make those obvious choices.
NFL coaches aren't going to suddenly be more inclined to go for it. Just look at the fascinating levels of stupidity in places like Cleveland, Buffalo, Carolina, Oakland, etc. where they are so risk averse it literally loses them games because they can't make those decisions correctly. There are only 3-4 teams who would see the advantage the rules gives them and exploit it as much as possible, New England, New Orleans, etc. the smartest teams in the league on the sidelines.
The QB penalties are another issue altogether. They wouldn't drastically increase with the rule anymore than expected. The NFL needs to address them in general, not hold of changing rules because of the fear that more incidents might pop up. The refs need to start judging intent and viciousness of hits, and not have all the contact under one blanket and judge a grazing of the helmet on an unstoppable attempt to block the pass (the play that cause Seattle to lose to Miami) different from a guy trying to tear a QB down by the head (See: Ndamukong Suh's career).
You can't do much to change automatic 1st down penalties unfortunately. Roughing the passer you can tighten up and make correct calls sure, but you can't do anything about pass interference or defensive holding. If you change those to 5 yards and no automatic 1st you will get defensive backs just tackling guys if they get a step on them to have a do over play. It is kind of like last week when a player got horse-collared to prevent a touchdown. That play should be an automatic touchdown rather than half the distance to the goal which ended up being two freaking yards. There is no elegant solution to fix the penalties on pass interference since granting an automatic touchdown would be nonsense and impossible to judge since who knows if the player would have caught the ball. The only inbetween would be a 10 yard penalty and an automatic 1st which still doesn't address the auto 1st issue.
I suppose the answer is better officiating or more review.