Most center surveillance radars have a range of 200 - 250NM (ARSR-3, ARSR-4, AN/FPS-117, AN/FPS-67B). Secondary beacon radars have a range of about 190NM for 1090ES equipped transponders.
You are correct in assuming most high altitude center control ops, for aircraft in cruise, rely heavily on MODE-S data. This is transponder data and not primary radar echo return data.
Terminal radar, the kind you see at your local airport, mostly relies on primary radar data. But at a shorter range (~50NM).
The reasons for the difference are many, but come down to accuracy and overlap. Center controllers use a mosaic of data from multiple radars that must average primary returns, this leads to slight disagreements on the true location of the aircraft. The MODE-S data is constant though, so it is preferred. In terminal environments, there's usually a single radar set. So the primary data is more useful in terms of accuracy for spacing the aircraft (they can pack them in tighter more safely). Terminal radar sets also have a higher scan rate.
MH370 was over the Gulf of Thailand and was under coverage of about three different radars. Even if the transponder was turned off, primary return data would still be available for the track. CrimsonAvenger has a valid point, but the last known location of the flight was far off shore and at a cruising altitude. So we could possibly speculate that line of sight was not a big factor.
There's a lot of big mysteries and speculation at this point, but we just need to give it time. They will eventually find the wreckage and hopefully determine they cause. There are many historical crashes that required more searching than has been applied to MH370 (AF447). In the meantime, grab some popcorn and enjoy the conspiracy theories...