Short answer: Not necessarily.
Long answer: The "bars" display shows a single number, quite coarsely. But to actually understand your reception conditions, there are two numbers you'd really like to know.
One is the absolute signal strength. That's what most phones display on their bars display. But there's no industry standard indicating what "one bar" means, or "two bars" means, so comparing the number of bars between phones of different models, even from the same manufacturer, doesn't tell you anything at all. One phone showing four bars and another showing two bars may actually be displaying the same value for the signal strength.
The other number is called EC/I0 (pronounced eee-see over eye-not) and it refers to the amount of the signal which is usable by the phone. In CDMA, every phone which is currently in a call using a given carrier frequency looks like noise to all the other phones using that carrier frequency. This is the major contributor to what is known as the noise floor. The difference between the total signal strength and the noise floor is usable signal, known as EC/I0.
The problem is that you really need to know both numbers to perform a scientific comparison of phones, and you need to know them to much more accuracy than five or six steps, which is all the "bars" display gives you.
The EC/I0 value can never exceed the absolute signal strength, but it can be far less as the cell becomes busier with other calls and the noise floor rises.
The problem with displaying the absolute signal strength is that it doesn't tell you enough. Even with "four bars", if the cell is overloaded then the EC/I0 value would be too low to support a call. On the other hand, with zero bars, if the cell is not busy then there may still be sufficient EC/I0 to support a call.
The problem with displaying the EC/I0 value instead is that it fluctuates very rapidly, since it is load dependent. It becomes very difficult to explain to a non-technical user why their phone display changed from four bars to zero bars and back to four bars again within a 30 second period, while they're sitting still, which can easily happen. It might convince them that their phone is malfunctioning, even though it is actually acting properly.
In any case, even knowing the absolute EC/I0 value to a sufficient degree of precision doesn't tell you everything you need to know. The state of the art is improving with each generation, and the receivers are getting more sensitive. One phone may be able to carry a call with a certain low EC/I0 value while another older phone, or one from a different manufacturer using different silicon, might drop a call even though its EC/I0 value is larger.
The joker in the deck is that this all tells only half the story, because all of it is concerned with the forward link. But a successful call also requires a reverse link from the phone to the cell, and that's entirely separate. Even if both the signal strength and EC/I0 values are sufficiently high to permit a phone to carry a call on the forward link, the environmental conditions might be such that the reverse link won't work. And there's no measurement the phone is capable of making which will tell you that, because the phone itself doesn't know!
Don't take the "number of bars" display on the phone too seriously. It's much too coarse and it contains far too little information. You can't use it to perform scientific comparisons of phones.