. . . engine will crank, like normal . . . but won't turn over . . .
Good. That's what I meant about using the term "turn over" differently. To many people, "turn over" means the engine turns, or cranks.
To answer your previous question, yes. As long as the starter is spinning the engine round and round, you can measure the compression. That's a good thing to do. You might Google and read up on "dry" and "wet" compression and measure both.
The fundamental rule of engines is that if it has compression, fuel and spark (timed correctly), it will run. Once you show you have good compression, it's time to check the spark.
People have a tendency to check the spark by pulling a wire and holding it 1/4" or so from a grounded engine part. I believe this is a bad idea and sometimes damages a perfectly good spark coil. For a spark to jump farther than .035" takes proportionally higher voltage, and excessive voltage leads to internal arcing in the coil. I prefer to connect a spare spark plug to the wires, and tie it securely to ground with a wire.
Once you have compression and spark, it's time to spray starting fluid into the carb. If the engine fires on starting fluid, that suggests you may have a fuel system problem.