Yes, ez3in1 Do can rumble while playing gba game. Different from the gba original rumble port (GPIO), ez has its own rumble port like what #2 said. And also the ez rumble port has some slight difference between ez3in1 and ezode. So we can't use the rumble tutorial EZteam supportting for ezode directly in ez3in1.
I've listed the detail in another post, and make an example code to support rumble in all of GPIO, ezode, ez3in1. You can see that.
https://gbatemp.net/threads/gamecube-gba-rumble-games-and-rom-hacked-rumble.589863/post-10236322
And I've also used this code in my rom hack project (a chinese translation project of Pokemon Pinball Ruby&Sapphire jp). You can see the rumble codes in /src. Or use this patch to run in your ez3in1 to experience its rumble. Here is my projct link:
https://github.com/Wokann/PokemonPinballRubySapphire_CHN
If you want ez3in1 to play the gba game which original has rumble function (GPIO), for now you may find the code where it use GPIO, and insert the ez
rumble port after it to active rumble in ez3in1. (ezode dont have this worry, cause ezode support both original rumble port (GPIO) and ez rumble port.)