I use Gmail and Outlook 2010 and have never had any issues with it. I’ve been using it for over seven years, and had a new PC three years ago so set it all up from scratch again.
I have four different email addresses on my Outlook programme (general personal Hotmail one, my own work email, and two client emails), and all work fine. I have had issues with getting them to work when first adding them, but once I’d worked it out (the issues were my fault), I find it very convenient having them all in one place. I even have different notification tones for each email, so when I’m transcribing I know whose email it is
I am presuming as I have an older version, that would also be a problem with Gmail, but I haven’t come across it. Not much help to you I’m afraid, but I shall follow any further replies with interest.
Previous to using Outlook, I used to use Windows Live Mail, and had three accounts on that, but I found it rather basic so changed to Outlook when I had my new PC.