The short answer is no, different speakers, cabinets, driver and crossovers combos will offer a different load and thus present a different "challenge" if you will for a given amp.
For instance you could take a sealed box two-way 10" speaker lets say and simply put in a 1 ,2 and 3 cubic foot box and you'd have different frequency response and the amps would see a different load of sorts if only by a little in each box size.
In a ported design there would be no back pressure in the cabinet to slow down the driver movement and this would probably be an easier load to drive but harder to control. Most ported designs are tuned between 30-50hz and frequencies below the port tuning become barely audible even less than 10hz below the tuned frequency.
Also we need to take into account the QTS and FS of the driver being used. All driver/box combinations provide a usually large impedance peak somewhere in the LF region. This is to say an 8 ohm (woofer) driver is not 8 ohms from say 20-400hz, there will be a peak or more than one and it may go quite high. Take a look at the link below and scroll to the bottom of page 4 and see the frequency vs impedance graph. The LF peaks for this 8 ohm category speaker go to near 30 ohms. The amp isn't going to do much when the load is 30 ohms but also won't get "hurt" or have a propensity to overheat if you will like it might if the load went down to 1 or even less than 1 ohm.
Also I use a passive horizontal bi-amp in my system. This means one amp drives the left and right HF sections of my speakers. There is no crossover before the amplifiers, just the ones in the speakers. The amplifier receives the full audio spectrum from the line stage (20Hz to 20KHz) but only frequencies above and near the 2.5KHz speaker crossover are "loaded" thus the amp runs very cool and the peak lights when they rarely light are lit by midrange events like a snare drum, guitar twang or loud piano/keyboard note but NEVER from a bass note or kick drum etc.
ET
http://www.madisound.com/catalog/PDF/RM6K-v2.pdf
