The counter is rated to count up to 2.6 GHz, but at that frequency, there must be quite a lot of signal going into it. At 1GHz, the rated sensitivity is 10mV which is -27 dBm, and the impedance is 50 ohms. This is a high level of signal. To count a signal off-air, you would need to use a proper antenna and put the antenna very close to the transmitting antenna. It is likely that at 2.4 GHz, the sensitivity is worse than at 1 GHz, so we might assume that signals need to enter the counter at about -15 to -20 dBm, which is a fairly strong signal.
You should be able to count a spread spectrum signal as well as any other depending on the protocol used. A counter of this type will end up counting the average signal frequency and this average will depend on the modulation. If the modulation is entirely symmetrical around a carrier, such as with analog FM for example, then the counter averages the frequency to the center frequency of the signal which happens to be the carrier. If a spread spectrum modulation is applied to a carrier, the average frequency is still counted and this average is certain to be somewhere within the bandwidth of the signal itself, perhaps not exactly at its center though.
The larger problem with many data signals is that they are not transmitting steadily at a constant power, so a frequency counter may not capture enough cycles of signal within its timing gate to count anything useful. Many protocols have the transmitter turning on and off rapidly over time. GSM is an example where the basic GSM voice call has the transmitter turning on and off very rapidly at a 220 Hz rate (approx) following a TDMA protocol. The transmitter only stays on for a very short time (can't remember exactly, but I think it was about 570 microseconds per burst). CDMA signals, including WCDMA, vary their power a great deal as they transmit and some of them also burst their signals vs time. I'm not sure how WiFi signals behave, but they may also burst their transmitters on and off rapidly, making it difficult for a counter to complete its count correctly.
If the counter is showing 0 then the problem is probably not enough level. In this case, you must try and couple a lot of signal into the counter and if you can't make a direct coax cable connection to the transmitter you are measuring, you must use a proper 2.4 GHz antenna and bring it very very close to the transmitter. If the counter shows a number but the number is rubbish, then it is quite possible that the signal you are trying to measure is pulsing on and off and/or is varying a great deal in amplitude vs time. The only thing you can do is shorten your gate time to the absolute minimum that the counter is capable of and hope to capture one burst. Otherwise there isn't much you can do. I think that it is hopeless for GSM since each burst is too short for your counter's minimum gate time.