You risk one play to gain one play, and the chance it pays out is almost certainly far north of 50%. The expected value is positive.
Ignoring what they actually did after that, let’s examine what happens if you run every time. I don’t remember how much time was left, so let’s say 2:30 and 5 seconds per play. (Runs for zero are quick.) In all cases, once you get 1st & 10 you run it four times for no gain and turn it over and downs.
Decline penalty, fail to convert:
Lose a yard, burn a time out, lose a yard, burn a timeout. The clock is now stopped at 2:20 on fourth down.
Decline penalty, convert:
Gain a yard, burn a time out, lose a yard, burn a timeout, lose a yard, 2:00 warning. Lose a yard, then turn it over on downs around 1:15.
Accept penalty:
Lose a yard, burn a time out, lose a yard, burn a timeout, lose a yard, 2:00 warning. Turn it over on downs with 1:55 left.
In all cases, the Packers are left with no timeouts. The only variable is when the Packers get the ball. Let’s assume the 70% success rate handing the ball off on 4th and 1 holds true for our 2nd and one situation. (You could fairly challenge this assumption, but it seems reasonable.)
70% chance they get the ball at 1:15
30% chance they get the ball at 2:20
or
100% chance they get the ball at 1:55
I’m taking that risk. 1:55 is more time than Aaron Rodgers needs. I don’t see a meaningful difference between that and 2:20. Honestly 1:15 is still too much time to give him, but it’s way better than 1:55.