If you don't have a placard, in WDW generally (not just the parks), you need to either drop off grandma & the ECV *OR* park directly next to the hc parking (if you can, not always possible). This is necessary as the only way to safely access wherever you are going, in my experience, is via the hc parking. If you park anywhere else and take the ECV out of the car there, grandma will be taking the parking lot grand tour, below driver's eye levels, pathetically trying to make her way over to the hc parking so she can use the curb cuts and ramps. I felt this was dangerous, and it was a large reason why I got a placard (also, I realized that it would solve my problem of not being able to go to certain places at home that didn't have a place to sit near the door, which prevented me from being dropped off & picked up).
Personally, I recommend locating an application for a placard for your state. Your grandmother very likely is eligible (mine has one). If you just wanted to get one for the trip, you can get a temporary one. There aren't that many "medical" (non-hc) spots in the medical parking, and with the ECV, it is just easier to have options in terms of what is easier/safer for your family and your grandmother in any given parking/drop-off situation. If you don't need to use it, you won't but if you do, you will have it.
Remember, DO NOT park in the main portion of any lot with the ECV w/o first ascertaining that you can safely get to the curb cuts/ramps. Not an issue with a manual wc but it is with an ECV and I imagine with a motorized wc. I am paranoid about this bc I almost got hit in the WL lot in my ECV.

Cupcake