Not exactly. A cell booster itself isn’t affected by rain fade, although dense rains can interfere with cell reception in general. Remember, a cellular signal booster can only amplify the signals it finds. If the signal is weakened by heavy rain, a booster is going to be less effective. If you have decent reception outside and the construction of your home makes it hard to get good reception inside, there’s no reason to worry about rain fade.
For the most part cellular signals themselves are very resistant to fade. They are at the relatively low frequencies of 700-1900MHz, unlike satellite signals that are up in the gigahertz range. As those frequencies get higher like that, you find that rain fade is an increasing problem.
Personally I have only experienced rain fade with cellular on one occasion and it was during a period of very heavy rain. At that point, I saw my cell signal drop from 5 bars to no service. At the same time I lost all over-the-air antenna TV as well as satellite, so clearly we were talking about some very heavy clouds.
If you feel you are experiencing rain fade or something that looks or feels like it, I would start by checking all the connections on your cable to make sure that they are nice and tight and free from corrosion. More likely what looks like rain fade is actually signal loss due to poor connections.