No, it's a bit more complicated than that. If the phone is GSM and has the correct bands, then it will work properly on the right GSM carrier. If the phone is GSM but does not have the correct bands/frequencies, then it may only work partly (i.e. voice, but only slow Edge/3G data). It just depends on what phone and which carrier you are talking about.
CDMA phones will not work on GSM carriers unless it is made specifically to do so (e.g. the Sprint Note 3 (CDMA) can apparently work on T-Mobile, which is GSM), which most CDMA phones are not. An unlocked CDMA phone should be able to be used on other CDMA carriers though.
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