Yes you can!
This was confirmed by Maxis with a community wide email announcement on the 11th of April 2013 and has since been rolled out with the Mac release of SimCity:
To Our Fans,
SimCity will be coming to the Mac on June 11 as a digital release via Origin™. If you have purchased SimCity for PC, either as a physical or a digital copy, you will receive the Mac version as a free digital download on Origin on June 11.
Via Origin, SimCity is cross-platform compatible, so all players will be able to play together across the same servers. You will be able to play both versions with the same Origin account, allowing you to seamlessly continue cities, achievements and leaderboard progress across the PC and Mac.
If you have purchased SimCity for PC, the Mac version has already been added to your Origin account. On your “My Games” page, hover over SimCity and click the info button. You will then see SimCity on Mac in the “Add-ons & Bonuses” section. You will be able to download and play the Mac version on June 11.
The post on the EA forum that you linked (which seems to have died) did seem to indicate that this is the case, more specifically, that if you purchase the game via Origin, you will be entitled to play the game on either platform once the Mac version is released.
The EA platform Origin does state that licenses for games available on both platforms will be transferable, though doesn't explicitly mention SimCity.
One new feature will be of particular interest for gamers who play on both PC and Mac machines: dual-platform play. For select EA games (that are available on both PC and Mac), you can buy a title once on Origin, and when you log into Origin on either Mac or PC, that same game will appear in your newly unified (Mac/PC) My Games library.
This will likely work in the same manner as Steam, in that once you own a license key for the game, you can then play that game on all supported platforms.
If your city is out of power for whatever reason it seems to take a while after you get a power plant online for power to reach the entire city. First a power plant has to get workers, then after that it seems to take a while before it actually starts supplying power.
Buying power from other cities may be buggy. I played a city for several hours buying power from neighboring cities; then saved and reloaded that city the next day only to find the city without power despite power still being available in the region (it is possible that not enough power was available) so I broke down and built a power plant and observed the city slowly get powered up.
Best Answer
EA is protective of their products and missing functionality on a patched game is unusual. It's possible you may not have an authentic copy.
EA delivers games using their Origin client, regardless of how you purchased your copy. If your copy is authentic you should be able to find it listed in your 'My Games' section of the Origin distribution client since EA would register your copy there. The Origin client is a free download: https://www.origin.com/en-us/download. Once you download it, you'll need to associate it with your purchase of the game, perhaps an email address you used with your coupon.
If your copy is authentic, it's possible it was disabled. At the time of your question, Maxis developers were making many improvements to SimCity and may have disabled the Region Wall as they worked on it. Try again now, I have been seeing it working in my copy this week.
That said, the Region Wall is useful for sending a message to a player not playing simultaneously since the messages aren't delivered until the user loads a city in that region. Otherwise, Origin Chat is good for messages to simultaneous players.