Not quite, you shouldn't try to run a high impedance mic into a lower impedance input if you care about your audio quality, But yes, you can use a lower impedance mic into a higher impedance input and the frequencies will pass.
A good analogy for people to think about on this subject is to think of a high impedance mic like a 2 inch water pipe under pressure trying to force it's way into a 1 inch opening. A lot of restrictions or impedance will happen, but a 1 inch water pipe into a 2 inch opening will pass the water with ease.
So no, if you have a 300 ohm mic for a 600 ohm mic input, there is no need for a matching transformer, but the reverse isn't true if you want your mics full audio potential to pass through especially if your mic is a high impedance like 2000 ohm.
So with lower impedance mics, it isn't necessary to exactly match the impedance input.