There are a lot of things to consider with this, especially if the two speakers are not identical. But let's assume that they are...
Theoretically, if you double the wattage then you'll get +6dB more sound level out. This is true (theoretically) regardless of if you take a single speaker from 200 to 400 watts, or go from one to two 200 watt speakers. In both cases the wattage doubles, so the sound level will rise +6dB.
In theory, theory matches practice. In practice, it doesn't.
Things are rarely so simple, and this is doubly so when it comes to sound. When you go from 1 to 2 speakers, you can get strange effects from the two speakers interfering with each other. Placement and orientation of the speakers can have a huge impact of this. In some cases, certain frequencies can completely cancel out while other frequencies will rise as much as +6dB. This is called "comb filtering". There are other related effects that could be a good thing (like a line array) or a bad thing, creating lots of really bad sound.
There is too much here to go into, but suffice it to say that if you want (effectively) a single speaker at 400 watts then that's what you should go with and not two 200 watt speakers. If you don't have that as an option, then I suggest that you place the speakers in such a way as the speaker coverage patterns don't overlap.
There is one thing that you didn't ask about, but I suspect you need to know, is how to calculate the apparent sound level given the wattage and speaker. Knowing this will greatly improve your chances of getting the right speaker/amp setup. Here are some rules/guidelines to know:
A 3dB change in sound level is considered "barely perceptible" to the human ear. A 6dB change in sound level is a doubling (or halving) of the power (watts), but is still considered a small change in perceived sound level.
If you double the distance from the speaker to the listener then the sound level will drop to 1/4th, or -12 dB.
Typical speech over a PA system should be somewhere in the 65 to 85 dB range. A loud rock concert might be as high as 115 dB. Movies are in the 100-105 dB range.
Speakers have "sensitivity ratings". A typical rating would be something like 85 dB/Watt/Meter. Meaning that if you put 1 watt into it, and measure it at 1 meter, you'll get 85 dB.
So here's what this means... Let's say that your speaker has a sensitivity of 85 dB/watt/meter, and you are 2 meters away and feeding it 1 watt. The sound you hear will be 73 dB. If you go to 2 watts then you get 79 dB. 4 watts = 85 dB. 8 watts = 91 dB. 16 watts = 97 dB. 32 watts = 103 dB. 64 watts = 109 dB. 128 watts = 115 dB.
Now if you move the speaker to 4 meters away you drop down to 103 dB. To get back up to 115 dB you need a 4x in power, or 512 watts. The point is, very quickly you get into some serious power levels for just a modest increase in sound level.
All of this is irrelevant to the topic of needing a sub woofer. If you need more low frequencies, then get a sub. If you don't, then don't.