Sure, as we have seen from the other answer and from documents like this, we can see that not only are wireless devices in high-radiation environments feasible, but they offer quite a long list of benefits.
If you really think about it, you will realize that any device humans have sent into space whether the device is an orbiter, satellite, rover, etc, they are all equipped with an antenna and an RF transceiver so they are capable of receiving and transmitting data. We already have our very own "IoT" consisting of these devices.
There is, however, an issue. IoT, or "Internet of Things" is a term that is commonly misused. An IoT device is a piece of embedded hardware that provides an interface to access its data over the internet. What you seem to be referring to is what is called a "mesh" network. This is a very important distinction to make.
There are many topologies and various technologies that can be used to create a mesh network. 802.11 (aka WiFi) is a good example, but there are other networks such as 802.15.4 (commonly known as Zigbee). In fact, the paper that I linked talks about using 802.11 devices in a mesh network on the surface of Mars in real-time while in orbit around Mars.
The distinction between a mesh network and "the internet" is very important here because the designers of the mesh network in the aforementioned paper are not required to make that network accessible by someone on the Earth's internet. Doing something like this on Earth would be fairly trivial, but from Mars it would be a completely different story.
The hardware necessary to make each device accessible from the Earth would be large, costly, and consume gobs of power. Also, consider the possibility for vulnerabilities in the code that runs on each device, you wouldn't want some miscreant to connect to it and cause some untold havoc.
Also, consider this: the latency from Mars to the Earth is bottlenecked by the speed of light. Depending on the distance between Mars and the Earth, you could be looking at a latency of 14 minutes (this is an average value, but you could see times between 4 and 22 minutes one-way, double that for round-trip time - both direct line of sight when Mars is not in solar conjunction with the Earth which is just about to happen this year, roughly between June 7 to June 21, 2015). This means that if you sat down and opened your laptop in the Mars settlement and tried connecting to
google.com, it would take several minutes just to connect.