She's never tried. In theory yes, it could well carry over; in practice Miki has simply never experimented in this manner, it's not something a chara does.
Smol Charas don't, but Miki-fused-with-Amu AKA Amulet Spade wields a giant paintbrush and had no problem throwing paint everywhere. Honestly, most of my assumptions about what Big Miki would be capable of psionically are based on what Amulet Spade would be capable of.
Getting the impression that's not really guaranteed to be the case anymore.
For this particular event, considering we can just tell Miki she's painting "for a full-body decal artwork" on the car, I'm not actually too concerned about Miki's mindset needing to be in the right place, moreso whether anything she makes would actually last a whole trip and back and could be done quickly.
EDIT:
If anybody does want to reopen the vote, some options I can think of are:
[ ] Pick up Utau, ask if they could borrow Nikaidou's car.
[ ] Ask Ami/Miki if they can make lasting Illusory car decals and/or a fake numberplate that will hold up for the trip.
[ ] Bring Ami along, ask her to actively hold up an Illusion on the car.
[ ] The old-fashioned way - smear mud on the numberplate and deface the body to make it harder to recognize, fix it later with Suu.