I'm not sure the number of people who would fall for it with or without an extra logo would be all that different...
The only phishing email I ever clicked was one about my Office 365 email getting lost. I was having email issues that week which made me click it faster than usual. Chrome saved me and blocked the site.
My grandmother-in-law was trying to tell me something to this effect last month; that her computer was "acting up" and someone called her "from Microsoft" and she hung up because the sheer coincidence scared her away from the PC.
Here is the same photo with mark ups.