Trump has said he wants to wait until the convention to "surprise" everyone with his VP pick, but it may be wise for him to roll the running mate out within a couple of weeks to send the message to the delegates that, "sorry folks, the Trump Train has already left the station and the Trump Train don't got no brakes."
I think it's more that >1237 delegates are now Trump true believers after his month of uncontested wins in delegate-rich states than it is about any fear of being seen as subverting the democratic process. So it might make it out of Rules but I would be shocked if the anti-Trump position got a majority on the floor unless he literally called for Kristallnacht against Mexican-Americans or something similar.
Honestly, I'm not sure that trump won't.