I have 4 RF units (each in the 1GHz band) that I would like to connect to one antenna. Can I simply wire all 4 RF connectors together and connect them to my antenna? Is the resulting signal simply the accumulation of the 4 individual signals?
Or do I need to make sure that only one of my 4 RF units is transmitting at the same time?
Of course you can wire them all together. They won't work but you can do it even though you shouldn't.
You will need to ensure a number of things. the first is that each transmitter needs to see a good load, usually 50 ohms otherwise it won't put out as much power as it should and won't work as efficiently as it should. If the load is a long way from the desired impedance it is possible that the transmitter may damage itself.
The second potential issue is that the transmitter may send it's output power into anther transmitter causing damage to that.
So you will either need to run them at different frequencies and use a multiplexer, that is a combination of filters that can be used to combine the different transmitters or else you will need to not only transmit at different times but also use a switch capable of handling the power and frequency of the signals.
There are further ways of approaching it, including iso-hybrids and iso-combiners but I've finished my post lunch coffee and should now do some work.