No. I was out of contract last year, and did this with my MXPE. Still have my UDP. I was even able to change to Unlimited texting without invoking a new contract.
For that matter, you can now walk into a VZW store, and buy a new phone on a payment plan, and still keep UDP. Not that they won't try to get you on a tiered data plan, but they won't force it.
The last part is subject to change, just like anything with them, now that we are "off contract."
I have looked at their pricing, and I could save money right now by going to tiered data, but I am probably going to wait. If I pull the trigger on a Pixel, I want to see how much of a data usage bump I see from full-size pictures going up to Google.