Yes, most cordless can, regardless of DECT.

No, DECT 6 doesn't define VMI capability, so just because it's DECT doesn't mean it has that feature. Just check the phone manual (usually available online) and see if it has VMI (voice mail indicator) light. The phone line gives a stutter tone if there is a VM and the phone would turn on the VMI. Some phone even has a dedicated, programmable VM button.

I love my Philips SE 659. It's a 2-line DECT 6 phone with 4 handsets and base speakerphone. Got it for $140 from eBay more than a year go.