Yes the rain especially heavy rain that is pouring down can affect the WiFi signal because when it's raining heavy the radio frequencies are absorbed and partially blocked by the rain droplets.
So if it's raining and you're trying to use WiFi especially public WiFi where you're a great enough distance from the WiFi signal then yes you'll likely notice a drop in the WiFi signal while it's raining heavy.
But you can also experience a drop in WiFi signal from your own home WiFi signal as well but shouldn't notice too much of a drop unless you're outside somewhere around your home during the rain.