I've beat you to the punch.. in December I started exactly what you suggest doing, I'm running an OD&D campaign as we speak, after picking up the Cyclopedia, the entire gazeteer series, and the Dawn of the Emperors, Hollow World, Wrath of the Immortals and Princess Ark boxed sets all in one lucky find.
You will discover that the system holds up remarkably well, and was (IMO) a far better RPG that AD&D (1st or 2nd) ever were. The Cyclopedia rules are in many way ahead of their time, their style being in some ways more like what systems are today than what they were back in the 80s.
A couple of bits of advice: read over the gazeteers (if you can get them) before you start the campaign.
Play the campaign PRECISELY to the rules specifications, ie. "old school", and make the whole thing a nostalgia romp. This will lead to some very silly moments, which will be good wholesome fun, but also don't be afraid to inject serious plotlines in there (the Gazeteers and boxed sets have lots of potential for serious gaming).
Make some real distinctions between the different "styles" of the game at different levels, based on what the old boxed sets were: levels 1-3 are for dungeon crawls, 4-14 for travel and experiencing the world of Mystara, lv. 15-25 are for governing dominions and playing out major events in the setting (to me this is a good time to kick into wrath of the immortals), and lv 26-36 is for running/influencing things on the national scale and preparing for the quest for immortality.
In my case the players are now averaging lv. 8-9, and are determined to play the game through to level 36 and beyond (immortality). Many have stated its their favourite campaign.
Nisarg