If that is a switch, as opposed to a coupler, then no, that will not work as you seem to want (connecting all three at the same time).
Since it is a switch, only one path is connected at a time. The single port side, which is what you are indicating the antenna would be connected to, is your source. With the antenna connected there, the switch would connect only one scanner at a time to the antenna. Changing to the next setting would disconnect that radio & instead connect a different one. If what you are wanting is to connect only one radio to the antenna at a time, and not use the other two, you could do that. But if you wanted to connect all three at once, you need a coupler, not a switch. While a coupler would work to connect three receivers to the same antenna, that would not be a good idea if you are transmitting on one or more of the radios.
As Thunderkight noted, if the radios are transceivers, as opposed to receivers only such as scanners, trying to transmit on one of them, with the other two connected to the same coupler, likely would cause damage to one or more of the units. Connecting the antenna to the single port side, and a radio to each of the other three ports would allow you to use one radio at a time for transmitting, selecting the active radio with the switch.
Edit to add: Look closely at the specs for your switch. I see it has a label of 1000 watts on it. If it isolates the output ports enough from each other, then you could use it to select one radio to utilize your antenna at a time,just not all three at once.
