Can I die from periorbital cellulitis if I ignore it?

Yes. Cellulitis usually needs antibiotics to heal. If not treated, the infection can spread rapidly, causing shock and death.
Yes. The eye is actually part of, not just connected to, your brain. This means that periorbital cellulitis is an infection in very close proximity to part of your brain. If it spreads, it can easily track up the blood vessels and/or nerves directly into your brain. Do not delay, seek care right away!