Amplifiers can help in some situations. If it is a low noise version and you have a signal at -120dBm and your receiver has a sensitivity of -125dBm but an internal noise figure of 6dB it would be impossible to hear that signal. If an amplifier has a 1dB noise figure and a 10dB gain then that signal will be -110dBm at the receiver and will be received. Noisy signals will be boosted to have less noise.
The problem are that most scanners get worse sensitivity when they are exposed to high signal levels at other frequencies. If it where a -60dBm signal 1MHz from the monitored one then the scanner could actually be desensed to -110dBm or worse when it is boosted to -50dBm and you would not hear a -110dBm signal and reception could be worse than without an amplifier.
You also have the overload/intermod issues that when the combined signals from all frequencies that are exposed to the receiver reach a certain level it creates mixing products that spread one signal to many other frequencies and you often hear 2 or 3 different transmissions at the same time on one frequency.
A preamplifier of the kind in the picture needs an internal level control to set it to the perfect level for that location and frequency band. If you have a preamplifier on the coax cable to an external antenna you can use a separate attenuator to reduce the signal before it goes to the receiver. 3dB-10dB total gain are probably what can be used in many cases without running into desense or intermod problems. SDS scanners already have a low noise amplifier built into them to overcome the high noise figure of their SDR receiver chip so there's not much help to get from using an additional external amplifier besides to overcome coax attenuation and stabilize impedance variations to antenna and scanner.
The better the scanners receiver are the more amplification it will tolerate. But most scanners have poor receivers and portables are among the worse. That's why you don't see many of that "stick them on the antenna connector" type.