I personally probably would as I get along with my boss and don't think he would ask unless absolutely necessary. But the fact is some employers will routinely take advantage of people willing to go the extra mile for no reward.
The last store I worked at, it would have to be pretty serious to get asked if you could come in earlier than normal. I prefer to stick to my hours if possible. Had told my previous bosses that I am more likely to come in and fill for someone, if I mention it previously that I would. Though, I would come in a few hours earlier than normal, if the shift that needs help, starts 2-3 hours normally before mine. Easier to accommodate that, over coming in for a shift that is completely out of the standard, like coming in to open a store, when you normally are there at closing.
My boss takes really good care of us. For her, I would absolutely be flexible. It solely depends on who is asking me. I’ve had previous supervisors that Id tell no in a heartbeat and probably a few other choice words.
Where I worked they wouldn't have asked that...but if I did work at a company where a boss asked me to come in early I'd probably ask for time and a half outside normal work hours.
With past jobs I've been asked to come in early. Most of the time I have. Because I needed the money and they already didn't pay me that much. So it was an opportunity to get a little more money to support my daughter. This was before my son was born. I changed professions after that.