Can the speakers "fry"? YES! oh god yes, done it on purpose multiple times...
The motherboard is covered in voltage regulators, resistors, amplifiers, etc to control signal/electrical noise, regulate voltage, amperage and power, and much more. The things you can do to manipulate electricity. I've see these components go bad, and in the wake cause a little damage to system wide catastrophic failure. But this is so easy to test for, as mentioned before.
New, fresh speakers require a break-in period. Like a car, keep the RPMs low and don't use cruise control for the first 500 miles. If you neglect this break-in period, you will get a burnt smell come strictly from the speaker itself. Has to do with all the glue and things getting really hot and the friction of rigid material. Nothing bad really happens, unless the speakers start some kind scratching noise or some other noise distortion, but this can be caused by blowing the speakers as well.
Thank you degree in electronic and electrical engineering...