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.