Unlikely, imo. Frequency response is simply a measurement of the range of frequencies over which a speaker can produce sound. It doesn't take into account things like dispersion, which can greatly affect how a speaker sounds in a given placement. In addition, while you may place boundaries on the level of variation across the frequency range (for example, 30 hz - 20 khx, +/- 3db), you don't necessarily know where in the range you're producing higher or lower volumes. An acoustic suspension enclosure and a bass reflex enclosure may share the same frequency response, but would most likely have different volume curve across the bass spectrum.
Is it worth mentioning the differences between speaker types, for example traditional, electrostatic, etc? Again, possible to find types with the same frequency response, but placed at the same position in a room they will not sound the same.
My .02,
bs
I think that if you review the previous posts in this thread that you may change your mind (or opinion) on what is the purpose of frequency response measurements, and if done with care, what they can tell you about the sound that will be produced from the speaker in question. They can, and do, provide a great deal more information than you're aware of, based on your post.
Your example of the Bass Reflex and Acoustic Suspension enclosures sharing the same frequency response and yet would have different "volume curves" across the bass spectrum is just plain wrong. If the frequency response is the same, then both will share the same "volume curve." In fact, in very simple terms, that's what a frequency response is, the "volume curve" of the speaker across the entire designated frequency span (often shown as 20Hz to 20kHz, but can go lower and higher).
Your last statement brings up some of the elements of the disagreement present in this thread. Keeping in mind that the original question was of an absolutely theoretical nature, that is, if two different speakers, that had an "identical" frequency response were placed in the identical spot in the same room, would they sound identical? I assumed that by being "identical" that would mean the frequency response taken on every axis. If this was the case, I suggested they would indeed sound the same. This ignores the fact that the probability of ever finding two different speakers with the "identical" frequency response is close to zero. The use of only on-axis response curves is, IMHO, of limited utility in determining what a speaker may sound like in a real world environment.
In your last paragraph you mention that electrostatic speakers (panel speakers?) and "traditional" (horns?) can have the same frequency response and yet, would sound different even if placed in the same position in a room.
The fact is, that if frequency response measurements were taken. not only on-axis, but also off-axis horizontally and vertically, you would certainly see major differences. If, by some change in the nature of Physics, they produced "identical" frequency responses using the protocol mentioned, then I believe they would certainly sound identical if placed in the same spot, in the same room.
FWIW: I certainly don't expect to see anything of the sort in my lifetime, so I'm not holding my breath.
Best Regards,
TerryO