Would an electroencephalogram detect a chip in you brain that is sending signals? To clarify the question, if you had a chip inside your brain that is sending bytes via wi-fii, bluethoot or other kind of waves, would the encephalogram detect anomalous activity?

Are the waves amplitude of normal brain electromagnetic activity very different from what a chip sends?
EEG electrodes are designed to record the electrical activity of the brain over the scalp. As @Bryan said the frequency of interest is usually less than 200 Hz, although it is possible to record up to 5KHz(e.g. BrainAmp). But we should keep in mind that even in the higher sampling frequencies, it is only recording the electrical potential over the scalp, while the communication devices you mentioned are using electromagnetic fields (Bluetooth and wifi) or radio frequencies (e.g RF modules) for communication, and seems irrelevant to compare these frequency ranges to the sampling rate of the recording device (apples and oranges).

However, any electronic device needs the power to run, and your device needs to be supplied with electrical source (i.e. batteries), and depending on how it is powered I think it would be possible to detected it with altered EEG on the electrodes above it. There exist passive implants that do not need external sources of energy to function, but they are not good enough to transfer data at the bitrates you mentioned. Bluetooth and wifi have a lot of power consumption and need batteries to function. 

To sum up, it depends on how your device is powered, and if there is a source of electrical activity, it will alter the EEG and you can detect it, although, you might not be able to say on which frequency exactly is working on (is it Bluetooth, wifi, RF, etc. ?).