The answer is yes, it can. Will it always make people sick? No. Dr. George Carlo explains that there is most definitely a biological response to what he refers to as Information Carrying Radio Waves (ICRW-energy fields from many wireless devices). When you're exposed to ICRW a process of adaptation and compensation occurs in your body. He has a great program that can help people adapt.
When you make a call, text, or use data, your phone sends and receives RF signals back and forth between its antenna and nearby cell towers. The radiation from Bluetooth and WiFi devices falls into the same basic range on the electromagnetic spectrum—between FM radios and microwave ovens—as the RF waves from cell phones. But because the distances traveled by WiFi and Bluetooth signals tend to be much shorter (between your router and your laptop, for instance, or your smartphone and your wireless speaker) the RF can be transmitted at a much lower power than from a cell phone, which could reduce the effect it has on living tissue.
Nevertheless, a group of scientists got together in the mid-2000s, calling themselves the BioInitiative Working Group. This group, which largely consisted of wireless radiation researchers, has written a harsh reply as feedback to the reports claiming that posed no health risks. The reply lists a wide range of health effects scientists at the European Commission have unfortunately either ignored or dismissed.