Almost. You probably need to add two more diodes across R1 and R2. These act as "catch" diodes to establish the DC bias on the two coupling capacitors.
This technique is called BTL - Bridge-Tied Load. If one end of your external load must be tied to GND, this will not work. If both ends of the external load can be floating, then this is a possibility. But since you have a 30 V supply, not explicitly necessary.
Another thought - You said that the signal being amplified is pulses. If that still is true (no sine or triangle waves), you do not need a linear amplifier. A pulse amplifier is much more simple, and the output transistors are saturated so there is very little heat generated in them. Attached is an updated version of driver I did last year. It can supply 200 mA peak output current by deleting R4. If that is not enough, the two transistors can be changed to power transistors or power darlingtons.
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View attachment 98065