You could, considering some projectors weigh right around 6 lbs or less, but unfortunately you're not affixing it to the "ceiling;" it'll be stuck onto the paint on the ceiling. I think it's a terrible idea, but you could, if you don't mind one day potentially seeing your projector in pieces on the floor .
Get a mount, they can be had for as little as ~$10. Good ones start at right around $70-90 on sale.
Internet Certified Electrical Engineer "I am just looking for an honest man."
You would want a tether attached more securely to catch the projector when/if it falls. With that, go for it. You could even use Velcro tape in order to allow repositioning.
I have attached go pro cameras to my gokart with 3M adhesive tape and never needed the tether. But I did have a tether.
Don't see the advantage of tape over screws, though. Screws into the ceiling are probably easier and less messy.
If what you have is a drywall or popcorn ceiling, those helix shaped drywall mount screws really work well. You don't need any solid wood to screw in to.
Simple logic says NO.
3M tech support say NONE of of there adhesive mounting tape is tested or approved from horizontal ceiling mounting as gravity is a constant and the product will fail. I had asked this about using the mounting tape to hold foam core panels..