It is possible. Not by any methods that you might be thinking though. but i'm not saying how you can do it either cuz it would ruin the topics about it.
Hmm... i don't think she'll remove Electrike anyway. I was going to say tha: "If she wanted to remove Electrike, she would have removed it already", but then... well, Gyarados was destroying everything for 11 episodes until Ame said "no", and removed it.
Still... Electrike usefulness in the 1st gym is pretty noticeable, since the AI is stupid and even after the Lightning Rod trigger message, Julia will continue to use Electric moves on you. And Toxic Spikes support from Trubbish is really helpful too.
The thing is: These two pokemons are not so "useful" later. Why stick with Garbodor when you can find a lot of other amazing poison types in Reborn. Why stick with Manectric when there are other electric pokes that are better than it?
Most people that used a Trubbish before, probably don't have a Garbodor right now. So, that's that.
Gyarados was removed because it was too good and it would stay too good for the rest of the game. After you get Magikarp to Level 20, that was it. The rest is game.