Yeah, pretty much*. That is: assuming you're talking about a system with the same overall efficiency, and most importantly: the same light distribution on the subject. E.g. comparing a focused spot (e.g. fresnel) vs. an unfocused omni light (e.g. softbox) will yield dramatically different results even for the same output power. So if you measure the illumination on a subject of a studio strobe of brand X with a gridded snoot to a strobe of brand Y with a softbox, you'll get different results even if their rated output power is exactly the same. Due to differences in electrical efficiency (bulb choice, discharge circuitry), aging (bulb, caps), even two strobes with the same rated output power, but different models, may very well show significant differences in effective on-subject illumination.
The rated flash power is really just an indication of what you might approximately expect from a strobe.
* Technically, half a stop over 200W would be 200W * SQRT(2) = ca. 283W. That's close enough to 300W to call the difference half a stop for all intents and purposes.
PS: power output of strobes we express as Ws or Watt-second, not W or Watt. Note the difference. W is continuous power without time dimension, Ws is an actual amount of energy delivered. Coincidentally, Ws is therefore the same as Joule (J), so a 200Ws strobe at full output power will dump 200 Joules of electrical power into the flash bulb.
A 200Ws strobe is (theoretically) 200 Watts over a period of one second (200 * 1 = 200), but can also be delivered as 200,000Watts during one millisecond (200,000 * 0.001 = 200), etc. The difference is notable, because if you don't account for it, you'll get very confused trying to compare continuous lights (e.g. LED panels) to strobes, and might decide that a 200W LED panel works just as well for your portrait project (for instance) as a 200Ws strobe - which will very much not be the case as you'll find the exposure times with the LED panel to be arguably far too long for a portrait! Just one small letter, but a meaningful difference.