Can an RLC network be defined that would behave in the same way as a theoretical loudspeaker? Since their behavior is frequency-dependent, would the values of R, L, and C also be frequency-dependent?
Yes, but you need to determine what properties of the loudspeaker you want the RLC network to mimic (model). You also need to specify the frequency range you are wanting the RLC network to be valid.
For example, if you want the network to model the electrical behavior of the speaker (e.g. have the RLC network have same voltage/current relationship over frequency) you would measure the speaker's impedance as a function of frequency and then design a circuit that has the same impedance vs. frequency. For lower frequencies (i.e. below the resonant frequency), the speaker will look like a series resistance and inductance. As the frequency increases, there will be resonances and the circuit becomes more complicated.
Here is a picture from Wikipedia showing an equivalent circuit for a mechanical phonograph horn that illustrates what form an RLC network could take when resonance is taken into account.
R, L and C are not frequency dependent; however, the impedance for L or C is strongly frequency dependent (\$Z_L=j2\pi f L\$ and \$Y_C=1/Z_C=j2\pi f C\$).
Um, why? Why would you want to do that?
Yes you can do what you want, sort of. At least you can approximate it. How close the approximation is depends on how complex you want to get. Everything that @madrivereric said is correct (so I won't repeat it here).
But as you try to get more and more accurate with your loudspeaker model things will get MUCH more complicated. For example, if you are trying to model a 3-way speaker with a horn loaded tweeter, a ported woofer, and a passive crossover then you have a huge problem on your hands.
As the level of complexity increases then you go back to my question of why. Educational uses aside, there is very little diagnostic info that such an RLC network can provide that a simple 4 or 8 ohm load resistor can't do. I would be interested in hearing of an application for this that I haven't considered.