Yes, but it is quite slow. Even 12 hours of charging might not be enough for someone's commute. For example, let's look at Honda's PHEV, the Clarity.

17kWh battery.

47 miles EV range.

Charge time @ 120V = 12 hours. It essentially can charge up to 4 miles of range per hour on a standard circuit in a US home. Cold weather? Your power needs go up, range goes down, and charge rate drops as well. 15 amps @ 120V EV charging is not practical for most EV owners, at this time, but you are correct that it is possible.

Why would you pick a PHEV for comparison? They are going to get a worse MPGe (because of the extra weight) and have a smaller battery (no catching up on charging during the weekend).

But more importantly, they can backup to gas so if you can only do 80% of your trip electric there is no real problem, you still are getting great fuel economy.

Slow and steady "wins the race" though. An average car is parked more than 12 hours a day. (The average is even closer to 23 hours than it is to 12 hours.) You easily cover the average commute even at 4 miles range added per hour (and as sibling post points out, some EVs do even better than that in a Level 1 charge) even just charging a car ~50% of the time that car spends parked.