You can have the SE unlocked provided the phone meets the eligibility criteria.
As to whether it will work on Verizon or that is something you can determine on the Verizon BYOD checker.
Unlocking does not guarantee that a phone will be able to work on a different network.
Thanks. I did do their BYOD checker and it said it won't work. But I wasn't sure if that's because the phone is currently "locked" to the Virgin Mobile network.
For what it's worth, I contact VZ support and they said the A1723 will NOT work on their network no matter what.