Nope even if you install it using aurora store it requires a Google account linked in play services (you can't even log into it manually!). So even on a device with play services but no Google account logged in I get an error logging in. On a Google free device it definitely won't work.
Beeper's clients never were open source. They were based on Apache 2 licensed Element. The new client won't be open source either, given how they don't even open source their server part (contrary to their matrix bridges).