I doubt it. What Elon did in cryptospace was either to make a quick and easily large amount of money or he was just having fun. He has no intentions to use a shitcoin like Doge in anything. If you look at his behavior, he first chose bitcoin and tried hyping then FUDing it to cause a pump and dump and he mostly failed since market didn't really react to his tweets even though he did it very well in coordination with the market direction. Then he did it to Doge and successfully cause a big pump and dump.
In comparison, adding Doge to Twitter would be a lot of effort!