Can computer speakers emit ultrasound?
Generally, yes (confirmed by both theory and experiment) though probably not as effectively as they can lower frequencies.

There are three primary factors:

1) The maximum frequency which can be produced by your source's DAC and associated anti-aliasing filters.  This is usually a bit below the Nyquist frequency for your effective sample rate, how far will depend on the sharpness of the filters.  There may also be spurious outputs centered on multiple(s) of the sample rate, but these are usually intentionally suppressed (and for most modern DACs, the actual conversion sample rate is many times the input one).  Unless you have a 96 Ksps system which is designed with filters to unlock that potential (rather than the more standard 96 Ksps data rate but aliasing filters still designed for a 48 Ksps one), this is probably going to be your primary limit. 

2) The maximum frequency which passes through the power amplifier.  For a traditional analog design this will be more of a rolloff than a sharp limit.  However, a "Class D" amplifier or something with digital processing may introduce its own sampling effects, and have its own strict filters to shield those.

3) The actual transducer response, and to an extent its acoustic environment.   Normal moving-coil midrange speakers aren't designed for even the top of the human hearing range, but they will typically still produce some output even beyond it.  In contrast, piezo transducers of various size could have resonant peaks at high frequencies, and actually produce more power there than at lower ones.

As a general comment, if you are planning to play with low ultrasound using consumer audio components, your challenge may be more on the receiving side than on the sending one, as the most common condenser microphones substantially roll off between 15-20 KHz (though a few of the smaller ones work higher).   In contrast, analog output silicon MEMS sensors are often good to much higher frequencies, being used off-label in bat detectors.  These are standard in smartphones, which appear to hear up to the limit imposed by their anti-aliasing filters.