How do I know if a given hardtail mtb frame is 'supposed' to have suspension forks?
Before suspension forks became commonplace, all mountain bikes were designed for a rigid fork. Fork length was sufficient to give good clearance between the crown and tire.

Suspension forks need to be longer than the minimum length rigid fork as obviously they need to compress without the tire hitting the crown. As suspension forks became available, frame manufacturers designed frames with higher headtubes to accommodate the longer suspension forks. Over the last few decades common fork travel length has gone from 20mm to over 150mm, and headtube height has increased accordingly. If you look at modern frames and frames from around 1990 it's easy to see how frame geometry has evolved. 

So, one can say that a frame with a moderate to large headtube to axle distance is designed for a suspension fork. Modern mountain bike frames are designed for suspension forks with a specific travel and headtube to axle distance that results in a desired head tube angle. XC bikes have less travel and shorter headtube to axle distance, downhill bikes have more travel and hence longer headtube to axle distance. There are still bike frames that are designed for a shorter rigid fork: many fat bikes and minimalist rigid single speeds for instance.

I believe the term 'suspension corrected' comes from the early days of suspension forks when the previously typical rigid fork length used was shorter than contemporary suspension fork length. To replace a suspension fork with a rigid one, a longer 'suspension corrected' fork was needed to preserve head tube angle. Note that modern bike suspension is designed to 'sag' slightly with a rider on the bike. A replacement rigid fork needs to be the same effective head tube to axle length as the'sagged' suspension fork, i.e. slightly shorter than the uncompressed length.

What you really want to find out is what headtube to axle length and head tube angle a given frame was intended to have. If you know the brand, model and year, do some searching on the web, you might be able to find out what model fork it originally came with and what the length of that fork was. If you know the intended use of the frame (XC, enduro etc,) you can look up common head tube angles and use geometry to estimate the headtube to axle length.