If they are willing to trade phone numbers (or get new numbers) then yes. When you upgrade, you can end up with the phone active on any line on your plan that you choose. That means that the new smartphone could certainly be placed on the line with the grandfathered data feature. What you won't be able to do is switch your existing phone numbers between lines, or move grandfathered features between lines, Verizon policy just doesn't allow it.
Once you get the phone activated on the line with the features you want, you could then ask for a new random number from Verizon (it might make the transition easier). It's free if you do it online through MyVerizon.
Good afternoon and thank you spottedcatfish and GTIMKV for your responses!
aznsolidus, this is a really good question, as I had to go over the scenario several times. The grandfathered Unlimited Data Plan will only apply to the line it is currently on. If any line currently does not have the Unlimited Data Plan, there is no way to get it, as you will have to choose from our current data plans. Therefore, if a line currently has a Smartphone with the Unlimited Data Plan, that line can upgrade to another Smartphone, or change to another Smartphone at any time, with the same Unlimited Data Plan. However, there is no way to swap the plan to a different phone number or phone line.