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Briar Desktop 0.5.0-beta released - macOS support, private groups and Briar Mailbox
(briarproject.org)
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Considering it cannot use push messaging by design, then not really.
But at least you can mitigate this by using a spare phone that you can leave plugged in (ie: at home) and act as a proxy using Briar Mailbox, so you can still receive messages even if the phone you carry with you isn't connected, as a way of saving some battery.