Kind of a dumb question, but if I am using two bass cabinets simultaneously with one head, do I add the wattage of each together to arrive at the total wattage the pair can handle? For example, if each cabinet is rated for 300 watts, can the two together handle a total of 600 watts from the head?
Yes, just remember that as long as the ohms rating of the cabinets are the same, the power that comes out of your amp will be evenly split between them. This can be a problem if you have cabs that have significantly different power handling capability.
For instance say you have a 210 cab that will handle 200-watts rms and a 410 cab that ill handle 400 watts. If you're driving those cabs with your 600-watt amp and you're pushing to max, it will send 300-watts to each cab. That's fine for the 410 cab because it can handle up to 400-watts, but can blow the speakers in the 210 because it can only handle 200-watts and you're sending 300-watts to it. But if you're using 2 cabs that have the same power-handling ratings, it should be no problem to add those two power-handling ratings up and use an amp of that will provide that total wattage rating.
In some cases, mine for instance, you can use an amp that will be able to send more power than they can handle if you don't run it at max. But you really need to pay attention and listen to what your are playing. With most amps, the master control is the "watts sent" control. I used my 800-watt amp to drive two 112 cabs that could handle 300-watts rms each. I plugged one into each channel of my dual-powerblock amp and it "could" feed those cabs as much as 400-watts each, which is 100-watts more than they can handle and would blow them. But I never got anywhere close to that power level because I didn't need anywhere near that much power to drive them to gig level in medium-sized venues where I used it.
I've since replaced those with my DNS210 cab which will handle 700-watts rms and I run my amp bridged with 800-watts "available" into 8 ohms. Just because that much power is available, doesn't mean that's how much I'm using. That cab will put out a max SPL of 134db with 700-watts and that's well above the threshold of pain. I typically run my master on my 800-watt amp at 10 o'clock on large indoor venues and 9 o'clock to 9:30 everywhere else indoors. So I'm not coming anywhere close to the max my amp will put out.
The one caveat you really have to bear in mind though when you have an amp that is capable of blowing the speakers you're using though, is how hard are you driving that amp. Will your speakers give you gig-level sound with a lower power setting or will you be tempted to keep turning it up to keep up with the rest of the band (guitarists are usually the ones who exacerbate this situation)? If you use speakers that have different power-handling capabilities, put the lowest power-handling cab on top closest to your ears so you can hear more easily when or if you are stressing them.
If you start to get anywhere close to dangerous levels for your speaker and you use a clean, clear sound, listen to what's coming out of them. If you start hearing farting noises, you are stressing your speakers and if you don't fix it at once, you will permanently damage them - don't wait for the end of he song, fix it now! If you use distortion or a lot of effects in your signal chain, it becomes geometrically more difficult to detect this stress on your speakers before you've ruined them.