Will the number still “work” while I am away? Meaning will folks be able to seamlessly leave voice mails and texts without issue?
When your eSIM is deactivated, your phone has no active connection to the carrier's network for that line. From the network's side this looks the same as a phone that's turned off or out of coverage. The carrier's switch sees the subscriber as unreachable and routes the call to voicemail the same way it would for any unanswered/unreachable call.
You can test this right now. Deactivate your work eSIM, then call your work number from another phone and see what happens. Note that deactivate is different than erase. By deactivating you are just turning it off temporarily and can easily check the box to turn it back on. If you erase it you'll need to download it again from your carrier (don't do that!)
As for being charged if instead you leave the work eSIM active and simply don't answer an incoming call, here is what T-Mobile says:
While roaming internationally, you won't be charged for voicemails left in your inbox if your phone remains powered off or in airplane mode. However, you will be charged for the following:
If your phone is on when you get an incoming call, even if you don't answer it and it goes to voicemail: The call is charged one minute for the call coming into the phone. (There are no charges at all if your phone is turned off.)
If your phone is off and receives incoming voicemails: When you turn it on while you are roaming internationally, the call is charged one minute for the voicemail coming into the phone.
From https://www.t-mobile.com/support/coverage/international-roaming-checklist