If you never meant a low frequency square wave, then you're not going to keep the speaker in one position for any length of time (which was your original hypothesis).
As the frequency gets higher and higher, it will look less and less like a square wave. The amplifier design will likely include a low pass filter somewhere in its design which will limit the fastest rise and fall time of the wave form. As the frequency gets close to the upper end of the audible range (say above ~12 to 15KHz or so) you'll probably find the amplitude of the signal reaching the speaker starts to roll off even if you send a maximum amplitude square wave to the input of the audio amplifier. Your square wave will at best look like a triangle or sawtooth wave and will be decreasing in amplitude more and more until it has virtually disappeared.
Some time ago I measured a square wave through a simple audio circuit (a typical amplifier in a modern laptop will perform rather better, but it still shows what will happen to a square wave as the frequency increases as it passes through a typical audio amplifier), and I still have the screen grabs from the oscilloscope. Let me demonstrate:
Waveform 1 (lowest frequency): http://photo.alioth.net/tmp2/b...
Waveform 2 (mid frequency): http://photo.alioth.net/tmp2/b...
Waveform 3 (highish frequency): http://photo.alioth.net/tmp2/b...
Waveform 4 (highest): http://photo.alioth.net/tmp2/b...
The square wave input was of identical amplitude for each of these, the only thing changed was the frequency. As I said the low pass filter in a typical amplifier found in a laptop's audio circuit won't start seriously attenuating the circuit anywhere near as low as this particular circuit, but it certainly will do the same in any case.
An audio designer who doesn't expect square waves at full design amplitude to go through his system is described by one word: "negligent". Typical 1980s analogue synthesizers often generated square waves, so you have to expect that some sound might contain a lot of square wave content. If a square wave not exceeding rated power can kill the Dell's speaker or audio circuit, then the product is defective and they should fix it under warranty, as warranties are supposed to fix defects caused by bad workmanship.