It can, but not easily. Your standard sub has a trimode amp inside it feeding both the sub and rears. The amp inside the Bose sub just feeds the sub (as the rears and fronts are fed off a seperate Bose amp (not part of the sub).
So the connectors are completely different and then you've got the problem of installing another small 2 x 25w amp for the rears (which you could do without replacing the sub at all). Although adding the Bose sub will give you more bass albeit as woolly as a woolly thing.
Are you sure it's the amp and not the speaker or wiring to the speaker?