I play guitar, and my amplifier is a Fender Mustang II combo amp. It has several pre-loaded effects and settings. One of the pre-loaded effects is an octaver, as they call it. What I was wondering is, since it has the octave effect pre-loaded into it, does that mean that it's safe to use without worrying about blowing out the cone or damaging the amp?

So, does this mean that the amp was made to handle low bass frequencies since it was designed with an octave effect pre-loaded into it? Does this mean I can plug a bass guitar into it? How does all this work?
Using a guitar with an octaver won't sound like a bass, plugging a bass in is very different from that and will damage it.
i think the "no bass into a guitar amp" idea is a bit of a myth personally. Ive never heard of anyone destroying their amp with a bass and in fact a lot of people use guitar amps (with bass cabinets) for their bass. Id say you're alright to use it for bass as long as you dont turn it up too loud. The issue is mostly if the speaker can handle the frequencies (which are different from a shifted guitar) of a bass for extended periods of time.
Bass once in a guitar amp won't kill it, the damage is gradual. Guitar amp with a bass cab is fine, it's the cab that's built for bass frequencies.
the only issue with using a bass with a guitar amp is the speakers. guitar speakers aren't made to handle the low frequencies that a bass puts out. at low volumes, you'll be fine, but once you start cranking up the volume, you'll wear through your speakers a lot more quickly than you would with a guitar.

so rule of thumb - bass is fine through a guitar amp, just don't use guitar speakers. use bass speakers.
Here's a thought: as most modelling amps come with built in cab sims, do they come with speakers voiced more flat than ones where the cab sound comes from the cab itself?
^No. Modelling amps do NOT come with cab sims. They almost exclusively model the preamp, at least, the Vypyr and the Mustang do not have cab sims. They have a speaker emulated out, but the signal going to the poweramp and speaker do not have a cab sim on them.

@TS: Running a guitar with an octaver wont hurt the speaker since a guitar pitch shifted down (or for the matter an 8 string guitar in E) wont damage the speaker since it wont have anywhere near as much fundamental as compared to a bass. Not only that, the most damage that basses cause to guitar speakers comes from slap and pop, and not regular playing. Slap and pop causes makes the speaker vibrate in extreme ways and that is generally what blows a normal guitar speaker. Even without slap and pop, a bass guitars longer scale and thicker strings causes much more fundamental harmonic to hit the speaker. Thats why bass>guitar speaker is bad, whereas guitar tuned down an octave is fine. Most 8 string players in E and F tuning use guitar speakers and not bass ones if that puts your mind at rest