With Laird RAMP radios, (CL4490/AC4490, CL4790/AC4790, LT1110, RM024) can I implement a design using just TX, RX and Gnd (three-wire interface) for UART?

Yes it is acceptable to implement a UART design which only uses TX (Transmit), RX (Receive) and Gnd (Ground)  However, it is strongly recommended that your hardware monitor the CTS pin of the radio.  CTS is taken High by the radio when its interface buffer is getting full.  Your hardware should stop sending at this point to avoid a buffer overrun (and subsequent loss of data).

You can perform a successful design without monitoring CTS.  However, you need to take into account the amount of latency the radio adds to the system, any additional latency caused by Transmit Retries or Broadcast Attempts, how often you send data, non-delivery network timeouts and interface data rate.  Polled type networks, where the Server host requests data from the Client host and the Client host responds, are good candidates for avoiding the use of CTS.  This is because no one transceiver can monopolize the RF link.  Asynchronous type networks, where any radio can send to another radio at any point in time, are much more difficult to implement without the use of CTS.